Regenerated branch
This commit is contained in:
Jose Luis Cercós Pita
parent
37d1696e16
commit
0a930d4c1a
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@ -21,6 +21,14 @@ SET(ShipExamples_SRCS
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)
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SOURCE_GROUP("shipexamples" FILES ${ShipExamples_SRCS})
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SET(ShipOpenCL_SRCS
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resources/opencl/matrixGen.cl
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resources/opencl/jacobi.cl
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resources/opencl/minres.cl
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resources/opencl/lsqr.cl
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)
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SOURCE_GROUP("shipopencl" FILES ${ShipOpenCL_SRCS})
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SET(ShipLoadExample_SRCS
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shipLoadExample/__init__.py
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shipLoadExample/TaskPanel.py
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@ -107,12 +115,18 @@ SET(SimRun_SRCS
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simRun/TaskPanel.ui
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simRun/clSim/__init__.py
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simRun/clSim/initialization.py
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simRun/clSim/Utils.py
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simRun/clSim/matrixGen.py
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simRun/clSim/BEMsolver.py
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simRun/clSim/evolution.py
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simRun/clSim/clUtils.py
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simRun/clSim/bem_jacobi_cl.py
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simRun/clSim/bem_minres_cl.py
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simRun/clSim/bem_lsqr_cl.py
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simRun/Sim/__init__.py
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simRun/Sim/initialization.py
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simRun/Sim/matrixGen.py
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simRun/Sim/computeSources.py
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simRun/Sim/fsEvolution.py
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simRun/Sim/BEMsolver.py
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simRun/Sim/evolution.py
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)
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SOURCE_GROUP("simrun" FILES ${SimRun_SRCS})
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@ -123,7 +137,7 @@ SET(SimPost_SRCS
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)
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SOURCE_GROUP("simpost" FILES ${SimPost_SRCS})
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SET(all_files ${ShipMain_SRCS} ${ShipIcons_SRCS} ${ShipExamples_SRCS} ${ShipLoadExample_SRCS} ${ShipCreateShip_SRCS} ${ShipOutlineDraw_SRCS} ${ShipAreasCurve_SRCS} ${ShipHydrostatics_SRCS} ${ShipUtils_SRCS} ${ShipWeights_SRCS} ${ShipCreateTank_SRCS} ${ShipGZ_SRCS} ${SimCreate_SRCS} ${SimRun_SRCS} ${SimPost_SRCS})
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SET(all_files ${ShipMain_SRCS} ${ShipIcons_SRCS} ${ShipExamples_SRCS} ${ShipOpenCL_SRCS} ${ShipLoadExample_SRCS} ${ShipCreateShip_SRCS} ${ShipOutlineDraw_SRCS} ${ShipAreasCurve_SRCS} ${ShipHydrostatics_SRCS} ${ShipUtils_SRCS} ${ShipWeights_SRCS} ${ShipCreateTank_SRCS} ${ShipGZ_SRCS} ${SimCreate_SRCS} ${SimRun_SRCS} ${SimPost_SRCS})
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ADD_CUSTOM_TARGET(Ship ALL
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SOURCES ${all_files}
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@ -143,6 +157,12 @@ INSTALL(
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DESTINATION
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Mod/Ship/resources/examples
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)
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INSTALL(
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FILES
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${ShipOpenCL_SRCS}
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DESTINATION
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Mod/Ship/resources/opencl
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)
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INSTALL(
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FILES
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${ShipLoadExample_SRCS}
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@ -15,6 +15,10 @@ nobase_data_DATA = \
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resources/examples/wigley.fcstd \
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resources/examples/wigley_katamaran.fcstd \
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resources/icons/Ico.xpm \
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resources/opencl/matrixGen.cl \
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resources/opencl/jacobi.cl \
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resources/opencl/minres.cl \
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resources/opencl/lsqr.cl \
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shipLoadExample/__init__.py \
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shipLoadExample/TaskPanel.py \
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shipLoadExample/TaskPanel.ui \
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@ -60,12 +64,18 @@ nobase_data_DATA = \
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simRun/TaskPanel.ui \
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simRun/clSim/__init__.py \
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simRun/clSim/initialization.py \
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simRun/clSim/Utils.py \
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simRun/clSim/matrixGen.py \
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simRun/clSim/BEMsolver.py \
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simRun/clSim/evolution.py \
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simRun/clSim/clUtils.py \
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simRun/clSim/bem_jacobi_cl.py \
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simRun/clSim/bem_minres_cl.py \
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simRun/clSim/bem_lsqr_cl.py \
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simRun/Sim/__init__.py \
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simRun/Sim/initialization.py \
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simRun/Sim/matrixGen.py \
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simRun/Sim/computeSources.py \
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simRun/Sim/fsEvolution.py \
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simRun/Sim/BEMsolver.py \
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simRun/Sim/evolution.py \
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simPost/__init__.py \
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simPost/TaskPanel.py \
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simPost/TaskPanel.ui
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@ -62,19 +62,38 @@ class FreeSurfaceFace:
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self.area = area
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class ShipSimulation:
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def __init__(self, obj, fsMeshData, waves):
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def __init__(self, obj, fsMeshData, waves, error):
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""" Creates a new simulation instance on active document.
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@param obj Created Part::FeaturePython object.
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@param h Sea water level.
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@param fsMeshData [L,B,N] Free surface mesh data, with lenght
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(x), Beam (y) and desired number of points.
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@param waves [[A,T,phi,heading],] Waves involved
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@param waves [[A,T,phi,heading],] Waves involved.
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@param error Relation between the minimum and the maximum Green's function values.
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"""
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# Add uniqueness property to identify Tank instances
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tooltip = str(QtGui.QApplication.translate("Ship","True if is a valid ship simulation instance",
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None,QtGui.QApplication.UnicodeUTF8))
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obj.addProperty("App::PropertyBool","IsShipSimulation","ShipSimulation", tooltip).IsShipSimulation=True
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# Store general data
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tooltip = str(QtGui.QApplication.translate("Ship","Free surface length in the x direction",
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None,QtGui.QApplication.UnicodeUTF8))
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obj.addProperty("App::PropertyFloat","L","ShipSimulation", tooltip).L=fsMeshData[0]
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tooltip = str(QtGui.QApplication.translate("Ship","Free surface length in the y direction",
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None,QtGui.QApplication.UnicodeUTF8))
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obj.addProperty("App::PropertyFloat","B","ShipSimulation", tooltip).B=fsMeshData[1]
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tooltip = str(QtGui.QApplication.translate("Ship","Free surface number of elements at x direction",
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None,QtGui.QApplication.UnicodeUTF8))
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obj.addProperty("App::PropertyInteger","FS_Nx","ShipSimulation", tooltip).FS_Nx=fsMeshData[2]
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tooltip = str(QtGui.QApplication.translate("Ship","Free surface number of elements at y direction",
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None,QtGui.QApplication.UnicodeUTF8))
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obj.addProperty("App::PropertyInteger","FS_Ny","ShipSimulation", tooltip).FS_Ny=fsMeshData[3]
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tooltip = str(QtGui.QApplication.translate("Ship","Relative error of the Green's function",
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None,QtGui.QApplication.UnicodeUTF8))
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obj.addProperty("App::PropertyFloat","error","ShipSimulation", tooltip).error=error
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# Compute free surface mesh
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self.createFSMesh(obj,fsMeshData)
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self.createVirtualFS(obj,fsMeshData,error)
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self.computeWaves(obj,waves)
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# Store waves
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tooltip = str(QtGui.QApplication.translate("Ship","Waves (Amplitude,period,phase)",
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@ -112,8 +131,8 @@ class ShipSimulation:
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def createFSMesh(self, obj, fsMeshData):
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""" Create or modify free surface mesh.
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@param obj Created Part::FeaturePython object.
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@param fsMeshData [L,B,N] Free surface mesh data, with lenght
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(x), Beam (y) and desired number of points.
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@param fsMeshData [L,B,Nx,Ny] Free surface mesh data, with lenght
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(x), Breath (y) and desired number of points at each direction.
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"""
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# Study input object
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try:
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@ -130,29 +149,17 @@ class ShipSimulation:
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FreeCAD.Console.PrintError(msg + '\n')
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return
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# Get areas and number of elements per direction
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L = fsMeshData[0]
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B = fsMeshData[1]
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N = fsMeshData[2]
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A = L*B
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L = fsMeshData[0]
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B = fsMeshData[1]
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nx = fsMeshData[2]
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ny = fsMeshData[3]
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N = nx*ny
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A = L*B
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area = A/N
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l = sqrt(area)
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b = sqrt(area)
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nx = int(round(L / l))
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ny = int(round(B / b))
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l = L/nx
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b = B/ny
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# Start data fields if not already exist
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props = obj.PropertiesList
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try:
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props.index("FS_Nx")
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except ValueError:
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tooltip = str(QtGui.QApplication.translate("Ship","Free surface number of elements at x direction",
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None,QtGui.QApplication.UnicodeUTF8))
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obj.addProperty("App::PropertyInteger","FS_Nx","ShipSimulation", tooltip).FS_Nx=0
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try:
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props.index("FS_Ny")
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except ValueError:
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tooltip = str(QtGui.QApplication.translate("Ship","Free surface number of elements at y direction",
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None,QtGui.QApplication.UnicodeUTF8))
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obj.addProperty("App::PropertyInteger","FS_Ny","ShipSimulation", tooltip).FS_Ny=0
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try:
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props.index("FS_Position")
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except ValueError:
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@ -172,6 +179,8 @@ class ShipSimulation:
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None,QtGui.QApplication.UnicodeUTF8))
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obj.addProperty("App::PropertyVectorList","FS_Normal","ShipSimulation", tooltip).FS_Normal=[]
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# Fill data
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obj.L = L
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obj.B = B
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obj.FS_Nx = nx
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obj.FS_Ny = ny
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pos = []
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@ -186,6 +195,68 @@ class ShipSimulation:
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obj.FS_Area = areas[:]
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obj.FS_Normal = normal[:]
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def createVirtualFS(self, obj, fsMeshData, error):
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""" Computes the number of required extended free surfaces.
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@param obj Created Part::FeaturePython object.
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@param fsMeshData [L,B,Nx,Ny] Free surface mesh data, with lenght
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(x), Breath (y) and desired number of points at each direction.
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@param error Relation between the minimum and the maximum Green's function values.
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"""
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# Study input object
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try:
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props = obj.PropertiesList
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props.index("IsShipSimulation")
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if not obj.IsShipSimulation:
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msg = QtGui.QApplication.translate("ship_console", "Object is not a valid ship simulation",
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None,QtGui.QApplication.UnicodeUTF8)
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FreeCAD.Console.PrintError(msg + '\n')
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return
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except ValueError:
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msg = QtGui.QApplication.translate("ship_console", "Object is not a ship simulation",
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None,QtGui.QApplication.UnicodeUTF8)
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FreeCAD.Console.PrintError(msg + '\n')
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return
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# Get dimensions of the elements
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L = fsMeshData[0]
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B = fsMeshData[1]
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nx = fsMeshData[2]
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ny = fsMeshData[3]
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dx = L / nx
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dy = B / ny
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# Compute maximum Green's function considering flat free surface
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Gmax = dx*asinh(dy/dx) + dy*asinh(dx/dy)
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# Locate the distance (number of free surface) to get the minimum required value
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Gmin = error*Gmax
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x = (L-dx)/2.0
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Nx = 0
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G = Gmin + 1.0
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while(G > Gmin):
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x = x + L
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Nx = Nx + 1
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G = 1.0 / (4.0*pi * x)
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y = (B-dy)/2.0
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Ny = 0
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G = Gmin + 1.0
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while(G > Gmin):
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y = y + L
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Ny = Ny + 1
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G = 1.0 / (4.0*pi * y)
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# Register computed data
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try:
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props.index("Sea_Nx")
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except ValueError:
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tooltip = str(QtGui.QApplication.translate("Ship","Number of repetitions of the free surface at x direction",
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None,QtGui.QApplication.UnicodeUTF8))
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obj.addProperty("App::PropertyInteger","Sea_Nx","ShipSimulation", tooltip).Sea_Nx=0
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try:
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props.index("Sea_Ny")
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except ValueError:
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tooltip = str(QtGui.QApplication.translate("Ship","Number of repetitions of the free surface at y direction",
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None,QtGui.QApplication.UnicodeUTF8))
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obj.addProperty("App::PropertyInteger","Sea_Ny","ShipSimulation", tooltip).Sea_Ny=0
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obj.Sea_Nx = Nx
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obj.Sea_Ny = Ny
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def computeWaves(self, obj, waves):
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""" Add waves effect to free surface mesh positions.
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@param obj Created Part::FeaturePython object.
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@ -215,21 +286,14 @@ class ShipSimulation:
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"""
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nx = obj.FS_Nx
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ny = obj.FS_Ny
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mesh = FSMesh(obj)
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# Create BSpline surface
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surf = Part.BSplineSurface()
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for i in range(1,nx-1):
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u = i / float(nx-1)
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surf.insertUKnot(u,i,0.000001)
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for i in range(1,ny-1):
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v = i / float(ny-1)
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surf.insertVKnot(v,i,0.000001)
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mesh = FSMesh(obj)
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surf = Part.BSplineSurface()
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pos = []
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for i in range(0,nx):
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pos.append([])
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for j in range(0,ny):
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u = i / float(nx-1)
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v = j / float(ny-1)
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point = mesh[i][j].pos
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surf.movePoint(u,v,point,i+1,i+1,j+1,j+1)
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pos[i].append(mesh[i][j].pos)
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surf.interpolate(pos)
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return surf.toShape()
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class ViewProviderShipSimulation:
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@ -694,3 +758,4 @@ def FSMesh(obj, recompute=False):
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obj.FS_Normal[j + i*ny] = faces[i][j].normal
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obj.FS_Area[j + i*ny] = faces[i][j].area
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return faces
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79
src/Mod/Ship/resources/opencl/jacobi.cl
Normal file
79
src/Mod/Ship/resources/opencl/jacobi.cl
Normal file
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@ -0,0 +1,79 @@
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/*
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* Copyright (c) 2011, 2012 *
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* Jose Luis Cercos Pita <jlcercos@gmail.com> *
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* *
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* This program is free software; you can redistribute it and/or modify *
|
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* it under the terms of the GNU Lesser General Public License (LGPL) *
|
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* as published by the Free Software Foundation; either version 2 of *
|
||||
* the License, or (at your option) any later version. *
|
||||
* for detail see the LICENCE text file. *
|
||||
* *
|
||||
* This program is distributed in the hope that it will be useful, *
|
||||
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
|
||||
* GNU Library General Public License for more details. *
|
||||
* *
|
||||
* You should have received a copy of the GNU Library General Public *
|
||||
* License along with this program; if not, write to the Free Software *
|
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* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 *
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* USA *
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*/
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/** Compute residuals of the solution stimator for a linear system.
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* @param A Linear system matrix.
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* @param B Linear system independent term.
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* @param X Solution estimation.
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* @param R Residuals.
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* @param n Linear system dimension.
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*/
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__kernel void r(__global float* A,
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__global float* B,
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__global float* X,
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__global float* R,
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unsigned int n)
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{
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// find position in global arrays
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unsigned int i = get_global_id(0);
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unsigned int j;
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if(i >= n)
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return;
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// Evaluate the row
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R[i] = B[i];
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for(j=0;j<n;j++){
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R[i] -= A[j + i*n]*X[j];
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}
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}
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|
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|
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/** Solve a linear system using Jacobi iterative method.
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* @param A Linear system matrix.
|
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* @param B Linear system independent term.
|
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* @param X0 Solution of the previous iteration.
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* @param X Solution of the actual iteration.
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* @param w Relaxation factor.
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||||
* @param n Linear system dimension.
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*/
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__kernel void jacobi(__global float* A,
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__global float* B,
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__global float* X0,
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__global float* X,
|
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float w,
|
||||
unsigned int n)
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{
|
||||
// find position in global arrays
|
||||
unsigned int i = get_global_id(0);
|
||||
unsigned int j;
|
||||
if(i >= n)
|
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return;
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// Evaluate the row
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X[i] = B[i];
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||||
for(j=0;j<n;j++){
|
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if(i == j){
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continue;
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}
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X[i] += A[j + i*n]*X0[j];
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||||
}
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X[i] *= w/A[i + i*n];
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X[i] += (1.f - w)*X0[i];
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}
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||||
186
src/Mod/Ship/resources/opencl/lsqr.cl
Normal file
186
src/Mod/Ship/resources/opencl/lsqr.cl
Normal file
|
|
@ -0,0 +1,186 @@
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/*
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||||
* Copyright (c) 2011, 2012 *
|
||||
* Jose Luis Cercos Pita <jlcercos@gmail.com> *
|
||||
* *
|
||||
* This program is free software; you can redistribute it and/or modify *
|
||||
* it under the terms of the GNU Lesser General Public License (LGPL) *
|
||||
* as published by the Free Software Foundation; either version 2 of *
|
||||
* the License, or (at your option) any later version. *
|
||||
* for detail see the LICENCE text file. *
|
||||
* *
|
||||
* This program is distributed in the hope that it will be useful, *
|
||||
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
|
||||
* GNU Library General Public License for more details. *
|
||||
* *
|
||||
* You should have received a copy of the GNU Library General Public *
|
||||
* License along with this program; if not, write to the Free Software *
|
||||
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 *
|
||||
* USA *
|
||||
*/
|
||||
|
||||
/** Get matrix column.
|
||||
* @param A Linear system matrix.
|
||||
* @param v Column vector (output).
|
||||
* @param col Column index.
|
||||
* @param n Linear system dimension.
|
||||
*/
|
||||
__kernel void column(__global float* A,
|
||||
__global float* v,
|
||||
unsigned int col,
|
||||
unsigned int n)
|
||||
{
|
||||
// find position in global arrays
|
||||
unsigned int i = get_global_id(0);
|
||||
if(i >= n)
|
||||
return;
|
||||
v[i] = A[i + col*n];
|
||||
}
|
||||
|
||||
/** Performs matrix column product by a constant.
|
||||
* @param A Linear system matrix.
|
||||
* @param c Constant.
|
||||
* @param col Column index.
|
||||
* @param n Linear system dimension.
|
||||
*/
|
||||
__kernel void prod_c_column(__global float* A,
|
||||
float c,
|
||||
unsigned int col,
|
||||
unsigned int n)
|
||||
{
|
||||
// find position in global arrays
|
||||
unsigned int i = get_global_id(0);
|
||||
if(i >= n)
|
||||
return;
|
||||
A[i + col*n] *= c;
|
||||
}
|
||||
|
||||
/** Compute residuals of the solution stimator for a linear system.
|
||||
* @param A Linear system matrix.
|
||||
* @param B Linear system independent term.
|
||||
* @param X Solution estimation.
|
||||
* @param R Residuals.
|
||||
* @param n Linear system dimension.
|
||||
*/
|
||||
__kernel void r(__global float* A,
|
||||
__global float* B,
|
||||
__global float* X,
|
||||
__global float* R,
|
||||
unsigned int n)
|
||||
{
|
||||
// find position in global arrays
|
||||
unsigned int i = get_global_id(0);
|
||||
unsigned int j;
|
||||
if(i >= n)
|
||||
return;
|
||||
// Evaluate the row
|
||||
R[i] = B[i];
|
||||
for(j=0;j<n;j++){
|
||||
R[i] -= A[j + i*n]*X[j];
|
||||
}
|
||||
}
|
||||
|
||||
/** Compute inner product between a matrix and a vector.
|
||||
* @param A Matrix.
|
||||
* @param X Vector.
|
||||
* @param Y Result.
|
||||
* @param n Linear system dimension.
|
||||
*/
|
||||
__kernel void dot_mat_vec(__global float* A,
|
||||
__global float* X,
|
||||
__global float* Y,
|
||||
unsigned int n)
|
||||
{
|
||||
// find position in global arrays
|
||||
unsigned int i = get_global_id(0);
|
||||
unsigned int j;
|
||||
if(i >= n)
|
||||
return;
|
||||
// Evaluate the row
|
||||
Y[i] = 0.f;
|
||||
for(j=0;j<n;j++){
|
||||
Y[i] += A[j + i*n]*X[j];
|
||||
}
|
||||
}
|
||||
|
||||
/** Compute inner product between a transposed matrix and a vector.
|
||||
* @param A Matrix.
|
||||
* @param X Vector.
|
||||
* @param Y Result.
|
||||
* @param n Linear system dimension.
|
||||
*/
|
||||
__kernel void dot_matT_vec(__global float* A,
|
||||
__global float* X,
|
||||
__global float* Y,
|
||||
unsigned int n)
|
||||
{
|
||||
// find position in global arrays
|
||||
unsigned int i = get_global_id(0);
|
||||
unsigned int j;
|
||||
if(i >= n)
|
||||
return;
|
||||
// Evaluate the row
|
||||
Y[i] = 0.f;
|
||||
for(j=0;j<n;j++){
|
||||
Y[i] += A[i + j*n]*X[j];
|
||||
}
|
||||
}
|
||||
|
||||
/** Create u vector for the next iteration.
|
||||
* @note u loads beta inside, you must compute
|
||||
* the norm and divide him.
|
||||
* @param A Linear system matrix.
|
||||
* @param u0 u vector from previous step.
|
||||
* @param v0 v vector from previous step.
|
||||
* @param u Looked u vector for next step.
|
||||
* @param alpha \$ \alpha_{i} \$.
|
||||
* @param n Linear system dimension.
|
||||
*/
|
||||
__kernel void u(__global float* A,
|
||||
__global float* u0,
|
||||
__global float* v0,
|
||||
__global float* u,
|
||||
float alpha,
|
||||
unsigned int n)
|
||||
{
|
||||
// find position in global arrays
|
||||
unsigned int i = get_global_id(0);
|
||||
unsigned int j;
|
||||
if(i >= n)
|
||||
return;
|
||||
// Evaluate the row
|
||||
u[i] = - alpha * u0[i];
|
||||
for(j=0;j<n;j++){
|
||||
u[i] += A[j + i*n]*v0[j];
|
||||
}
|
||||
}
|
||||
|
||||
/** Create v vector for the next iteration.
|
||||
* @note v loads alpha inside, you must compute
|
||||
* the norm and divide him.
|
||||
* @param A Linear system matrix.
|
||||
* @param u u vector for next step.
|
||||
* @param v0 v vector from previous step.
|
||||
* @param v Looked v vector for next step.
|
||||
* @param beta \$ \beta_{i+1} \$.
|
||||
* @param n Linear system dimension.
|
||||
*/
|
||||
__kernel void v(__global float* A,
|
||||
__global float* u,
|
||||
__global float* v0,
|
||||
__global float* v,
|
||||
float beta,
|
||||
unsigned int n)
|
||||
{
|
||||
// find position in global arrays
|
||||
unsigned int i = get_global_id(0);
|
||||
unsigned int j;
|
||||
if(i >= n)
|
||||
return;
|
||||
// Evaluate the row
|
||||
v[i] = - beta * v0[i];
|
||||
for(j=0;j<n;j++){
|
||||
v[i] += A[i + j*n]*u[j];
|
||||
}
|
||||
}
|
||||
|
||||
326
src/Mod/Ship/resources/opencl/matrixGen.cl
Normal file
326
src/Mod/Ship/resources/opencl/matrixGen.cl
Normal file
|
|
@ -0,0 +1,326 @@
|
|||
/*
|
||||
* Copyright (c) 2011, 2012 *
|
||||
* Jose Luis Cercos Pita <jlcercos@gmail.com> *
|
||||
* *
|
||||
* This program is free software; you can redistribute it and/or modify *
|
||||
* it under the terms of the GNU Lesser General Public License (LGPL) *
|
||||
* as published by the Free Software Foundation; either version 2 of *
|
||||
* the License, or (at your option) any later version. *
|
||||
* for detail see the LICENCE text file. *
|
||||
* *
|
||||
* This program is distributed in the hope that it will be useful, *
|
||||
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
|
||||
* GNU Library General Public License for more details. *
|
||||
* *
|
||||
* You should have received a copy of the GNU Library General Public *
|
||||
* License along with this program; if not, write to the Free Software *
|
||||
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 *
|
||||
* USA *
|
||||
*/
|
||||
|
||||
#ifndef M_PI
|
||||
#define M_PI 3.14159265f
|
||||
#endif
|
||||
|
||||
#ifndef _NG_
|
||||
#define _NG_ 16
|
||||
#endif
|
||||
|
||||
/** Compute \$G_{ab}\$ effect: \n
|
||||
* \$ G_{ab} = \frac{1}{4 \pi \vert \mathbf{r} \vert } \$
|
||||
* @param r Union vector \$ \mathbf{r}_{ab} \$
|
||||
*/
|
||||
float G_val(float4 r)
|
||||
{
|
||||
return 1.f / ( 4.f*M_PI * length(r) );
|
||||
}
|
||||
|
||||
/** Compute \$H_{ab}\$ effect: \n
|
||||
* \$ H_{ab} = \frac{\mathbf{r}}{4 \pi \vert \mathbf{r} \vert^3} \cdot n_b \$
|
||||
* @param r Union vector \$ \mathbf{r}_{ab} \$
|
||||
* @param n Element normal \$ n_b \$
|
||||
*/
|
||||
float H_val(float4 r,
|
||||
float4 n)
|
||||
{
|
||||
return - dot(r,n) / (4.f*M_PI * pow(dot(r,r),1.5f));
|
||||
}
|
||||
|
||||
/** Computes z coordinate due to the waves superposition
|
||||
* for a desired position.
|
||||
* @param w Array of waves.
|
||||
* @param p Point to compute.
|
||||
* @param t Simulation time.
|
||||
* @param nW Number of waves.
|
||||
* @return z coordinate.
|
||||
*/
|
||||
float waves_z(__global float4* w, float4 p, float t, unsigned int nW)
|
||||
{
|
||||
/*
|
||||
return 0.f;
|
||||
*/
|
||||
|
||||
unsigned int i;
|
||||
float z = 0.f;
|
||||
for(i=0;i<nW;i++){
|
||||
float omega = 2.f * M_PI / w[i].y;
|
||||
float k = omega * omega / 9.81f;
|
||||
float beta = w[i].w * M_PI / 180.f;
|
||||
float l = p.x*cos(beta) + p.y*sin(beta);
|
||||
z += w[i].x * sin(k*l - omega*t + w[i].z);
|
||||
}
|
||||
return z;
|
||||
}
|
||||
|
||||
/** Computes velocity potential due to the waves superposition
|
||||
* for a desired position.
|
||||
* @param w Array of waves.
|
||||
* @param p Point to compute.
|
||||
* @param t Simulation time.
|
||||
* @param nW Number of waves.
|
||||
* @return z coordinate.
|
||||
*/
|
||||
float waves_phi(__global float4* w, float4 p, float t, unsigned int nW)
|
||||
{
|
||||
/*
|
||||
float4 r;
|
||||
r.w = 0.f;
|
||||
r.xy = p.xy;
|
||||
r.z = 15.f;
|
||||
return G_val(r);
|
||||
*/
|
||||
|
||||
|
||||
unsigned int i;
|
||||
float z = 0.f;
|
||||
for(i=0;i<nW;i++){
|
||||
float omega = 2.f * M_PI / w[i].y;
|
||||
float k = omega * omega / 9.81f;
|
||||
float beta = w[i].w * M_PI / 180.f;
|
||||
float l = p.x*cos(beta) + p.y*sin(beta);
|
||||
z -= w[i].x*omega/k * cos(k*l - omega*t + w[i].z)*exp(k*p.z);
|
||||
}
|
||||
return z;
|
||||
}
|
||||
|
||||
/** Computes velocity potential gradient z coordinate
|
||||
* due to the waves superposition
|
||||
* for a desired position.
|
||||
* @param w Array of waves.
|
||||
* @param p Point to compute.
|
||||
* @param t Simulation time.
|
||||
* @param nW Number of waves.
|
||||
* @return z coordinate.
|
||||
*/
|
||||
float waves_gradphi(__global float4* w, float4 p, float t, unsigned int nW)
|
||||
{
|
||||
/*
|
||||
float4 r,n;
|
||||
r.w = 0.f;
|
||||
r.xy = p.xy;
|
||||
r.z = 15.f;
|
||||
n.x = 0.f;
|
||||
n.y = 0.f;
|
||||
n.z = 1.f;
|
||||
n.w = 0.f;
|
||||
return H_val(r,n);
|
||||
*/
|
||||
|
||||
|
||||
unsigned int i;
|
||||
float z = 0.f;
|
||||
for(i=0;i<nW;i++){
|
||||
float omega = 2.f * M_PI / w[i].y;
|
||||
float k = omega * omega / 9.81f;
|
||||
float beta = w[i].w * M_PI / 180.f;
|
||||
float l = p.x*cos(beta) + p.y*sin(beta);
|
||||
z -= w[i].x*omega * cos(k*l - omega*t + w[i].z)*exp(k*p.z);
|
||||
}
|
||||
return z;
|
||||
}
|
||||
|
||||
/** Computes \$G_{ab}\$ and \$H_{ab}\$ in the case that \$a = b\$ \n
|
||||
* \$ G_{ab} = \frac{1}{4 \pi \vert \mathbf{r} \vert } \$
|
||||
* \$ H_{ab} = \frac{\mathbf{r}}{4 \pi \vert \mathbf{r} \vert^3} \cdot n_b - \frac{1}{2} \$
|
||||
* @param positions Array of points of the free surface
|
||||
* @param w Array of waves data (Amplitude,period,phase,heading)
|
||||
* @param normals Element normals
|
||||
* @param I x index of the point to compute.
|
||||
* @param J y index of the point to compute.
|
||||
* @param L Free surface length in the x direction.
|
||||
* @param B Free surface length in the y direction.
|
||||
* @param dx Distance between element centers in the x direction.
|
||||
* @param dy Distance between element centers in the x direction.
|
||||
* @param t Simulation time.
|
||||
* @param nx Free surface points in the x direction.
|
||||
* @param ny Free surface points in the y direction.
|
||||
* @param nW Number of waves.
|
||||
*/
|
||||
float2 GH(__global float4* positions,
|
||||
__global float4* w,
|
||||
__global float4* normals,
|
||||
unsigned int I, unsigned int J,
|
||||
float L, float B,
|
||||
float dx, float dy,
|
||||
float t,
|
||||
unsigned int nx,
|
||||
unsigned int ny,
|
||||
unsigned int nW)
|
||||
{
|
||||
__private float4 P[9];
|
||||
__private float K[9];
|
||||
unsigned int i,j;
|
||||
float4 p = positions[I*ny + J];
|
||||
float4 n = normals[I*ny + J];
|
||||
float Dx = dx / _NG_;
|
||||
float Dy = dy / _NG_;
|
||||
for(i=0;i<3;i++){
|
||||
for(j=0;j<3;j++){
|
||||
P[i*3+j].x = p.x + (i-1)*dx;
|
||||
P[i*3+j].y = p.y + (j-1)*dy;
|
||||
if( (P[i*3+j].x > -0.5*L) &&
|
||||
(P[i*3+j].x < 0.5*L) &&
|
||||
(P[i*3+j].y > -0.5*B) &&
|
||||
(P[i*3+j].y < 0.5*B))
|
||||
P[i*3+j].z = positions[(I-1+i)*ny + (J-1+j)].z;
|
||||
else
|
||||
P[i*3+j].z = waves_z(w, P[i*3+j], t, nW);
|
||||
P[i*3+j].w = 0.f;
|
||||
}
|
||||
}
|
||||
// Get SPline surface coeffs
|
||||
K[0] = P[0].z; // k_{0}
|
||||
K[1] = 4*P[3].z - P[6].z - 3*P[0].z; // k_{u}
|
||||
K[2] = 4*P[1].z - P[2].z - 3*P[0].z; // k_{v}
|
||||
K[3] = P[8].z - 4*P[7].z + 3*P[6].z +
|
||||
3*P[2].z - 12*P[1].z + 9*P[0].z +
|
||||
-4*P[5].z + 16*P[4].z - 12*P[3].z; // k_{uv}
|
||||
K[4] = 2*P[6].z + 2*P[0].z - 4*P[3].z; // k_{uu}
|
||||
K[5] = 2*P[2].z + 2*P[0].z - 4*P[1].z; // k_{vv}
|
||||
K[6] = -2*P[8].z + 8*P[7].z - 6*P[6].z +
|
||||
-2*P[2].z + 8*P[1].z - 6*P[0].z +
|
||||
4*P[5].z - 16*P[4].z + 12*P[3].z; // k_{uuv}
|
||||
K[7] = -2*P[8].z + 4*P[7].z - 2*P[6].z +
|
||||
-6*P[2].z + 12*P[1].z - 6*P[0].z +
|
||||
8*P[5].z - 16*P[4].z + 8*P[3].z; // k_{uuv}
|
||||
K[8] = 4*P[8].z - 8*P[7].z + 4*P[6].z +
|
||||
4*P[2].z - 8*P[1].z + 4*P[0].z +
|
||||
-8*P[5].z + 16*P[4].z - 8*P[3].z; // k_{uuvv}
|
||||
// Loop around the point p collecting the integral
|
||||
float2 gh;
|
||||
gh.x = 0.0f;
|
||||
gh.y = -0.5f;
|
||||
for(i=0;i<_NG_;i++){
|
||||
for(j=0;j<_NG_;j++){
|
||||
float4 p_a;
|
||||
float u,v;
|
||||
p_a.x = positions[I*ny + J].x - 0.5f*dx + (i+0.5f)*Dx;
|
||||
p_a.y = positions[I*ny + J].y - 0.5f*dy + (j+0.5f)*Dy;
|
||||
u = (p_a.x - P[0].x) / (P[6].x - P[0].x);
|
||||
v = (p_a.y - P[0].y) / (P[2].y - P[0].y);
|
||||
p_a.z = K[0] + K[1]*u + K[2]*v + K[3]*u*v +
|
||||
K[4]*u*u + K[5]*v*v + K[6]*u*u*v +
|
||||
K[7]*u*v*v + K[8]*u*u*v*v;
|
||||
p_a.w = 1.f;
|
||||
gh.x += G_val(p_a - p)*Dx*Dy;
|
||||
// For some reason H is not well integrated
|
||||
// gh.y += H_val(p_a - p, n)*Dx*Dy;
|
||||
}
|
||||
}
|
||||
return gh;
|
||||
}
|
||||
|
||||
/** Compute Linear system matrix. Desingularized sources must taken into account.
|
||||
* @param A Linear system matrix.
|
||||
* @param B Independent term for velocity potentials.
|
||||
* @param positions Elements points.
|
||||
* @param areas Elements area.
|
||||
* @param normals Elements normals.
|
||||
* @param p Velocity potentials.
|
||||
* @param dp Acceleration potentials.
|
||||
* @param waves Array of waves data (Amplitude,period,phase,heading)
|
||||
* @param l Free surface length in the x direction.
|
||||
* @param b Free surface length in the y direction.
|
||||
* @param dx Distance between element centers in the x direction.
|
||||
* @param dy Distance between element centers in the x direction.
|
||||
* @param t Simulation time.
|
||||
* @param nx Free surface points in the x direction.
|
||||
* @param ny Free surface points in the y direction.
|
||||
* @param nFS Number of points in the free surface.
|
||||
* @param nB Number of points in the body (ignored yet, should be 0).
|
||||
* @param n Total number of points.
|
||||
* @param nSeax Number of repetitions of the free surface in the x direction.
|
||||
* @param nSeay Number of repetitions of the free surface in the y direction.
|
||||
* @param nW Number of waves.
|
||||
*/
|
||||
__kernel void matrixGen(__global float* A,
|
||||
__global float* B,
|
||||
__global float4* positions,
|
||||
__global float* areas,
|
||||
__global float4* normals,
|
||||
__global float* p,
|
||||
__global float* dp,
|
||||
__global float4* waves,
|
||||
float l,
|
||||
float b,
|
||||
float dx,
|
||||
float dy,
|
||||
float t,
|
||||
unsigned int nx,
|
||||
unsigned int ny,
|
||||
unsigned int nFS,
|
||||
unsigned int nB,
|
||||
unsigned int n,
|
||||
int nSeax,
|
||||
int nSeay,
|
||||
unsigned int nW)
|
||||
{
|
||||
// find position in global arrays
|
||||
unsigned int i = get_global_id(0);
|
||||
unsigned int j;
|
||||
int I,J;
|
||||
if(i >= n)
|
||||
return;
|
||||
// Get the point where we want to evaluate
|
||||
float4 p_a = positions[i];
|
||||
// Evaluate the row
|
||||
B[i] = 0.f;
|
||||
for(j=0;j<nFS;j++){
|
||||
// Get G,H for this pair of points
|
||||
float2 gh;
|
||||
float4 p_b = positions[j];
|
||||
float4 n_b = normals[j];
|
||||
if(i == j){
|
||||
gh = GH(positions,waves,normals,i/ny,i%ny,
|
||||
l,b,dx,dy,t,nx,ny,nW);
|
||||
}
|
||||
else{
|
||||
p_b = positions[j];
|
||||
gh.x = G_val(p_b - p_a)*dx*dy;
|
||||
gh.y = H_val(p_b - p_a, n_b)*dx*dy;
|
||||
}
|
||||
// In the free surface G goes to the linear system
|
||||
// matrix while H goes to the B term
|
||||
A[j + i*n] = -gh.x;
|
||||
B[i] += gh.y * p[j];
|
||||
// Compute also the terms of the virtual free surface
|
||||
// extension.
|
||||
for(I=-nSeax;I<=nSeax;I++){
|
||||
for(J=-nSeay;J<=nSeay;J++){
|
||||
if((!I) && (!J))
|
||||
continue;
|
||||
float4 p_c = p_b;
|
||||
p_c.x += I*l;
|
||||
p_c.y += J*b;
|
||||
p_c.z = waves_z(waves, p_c, t, nW);
|
||||
gh.x = G_val(p_c - p_a)*dx*dy;
|
||||
gh.y = H_val(p_c - p_a, n_b)*dx*dy;
|
||||
// In the extended free surface both terms goes to
|
||||
// the B term
|
||||
B[i] += gh.y*waves_phi(waves, p_c, t, nW) - gh.x*waves_gradphi(waves, p_c, t, nW);
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
94
src/Mod/Ship/resources/opencl/minres.cl
Normal file
94
src/Mod/Ship/resources/opencl/minres.cl
Normal file
|
|
@ -0,0 +1,94 @@
|
|||
/*
|
||||
* Copyright (c) 2011, 2012 *
|
||||
* Jose Luis Cercos Pita <jlcercos@gmail.com> *
|
||||
* *
|
||||
* This program is free software; you can redistribute it and/or modify *
|
||||
* it under the terms of the GNU Lesser General Public License (LGPL) *
|
||||
* as published by the Free Software Foundation; either version 2 of *
|
||||
* the License, or (at your option) any later version. *
|
||||
* for detail see the LICENCE text file. *
|
||||
* *
|
||||
* This program is distributed in the hope that it will be useful, *
|
||||
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
|
||||
* GNU Library General Public License for more details. *
|
||||
* *
|
||||
* You should have received a copy of the GNU Library General Public *
|
||||
* License along with this program; if not, write to the Free Software *
|
||||
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 *
|
||||
* USA *
|
||||
*/
|
||||
|
||||
/** Compute residuals of the solution stimator for a linear system.
|
||||
* @param A Linear system matrix.
|
||||
* @param B Linear system independent term.
|
||||
* @param X Solution estimation.
|
||||
* @param R Residuals.
|
||||
* @param n Linear system dimension.
|
||||
*/
|
||||
__kernel void r(__global float* A,
|
||||
__global float* B,
|
||||
__global float* X,
|
||||
__global float* R,
|
||||
unsigned int n)
|
||||
{
|
||||
// find position in global arrays
|
||||
unsigned int i = get_global_id(0);
|
||||
unsigned int j;
|
||||
if(i >= n)
|
||||
return;
|
||||
// Evaluate the row
|
||||
R[i] = B[i];
|
||||
for(j=0;j<n;j++){
|
||||
R[i] -= A[j + i*n]*X[j];
|
||||
}
|
||||
}
|
||||
|
||||
/** Compute inner product between a matrix and a vector.
|
||||
* @param A Matrix.
|
||||
* @param X Vector.
|
||||
* @param Y Result.
|
||||
* @param n Linear system dimension.
|
||||
*/
|
||||
__kernel void dot_mat_vec(__global float* A,
|
||||
__global float* X,
|
||||
__global float* Y,
|
||||
unsigned int n)
|
||||
{
|
||||
// find position in global arrays
|
||||
unsigned int i = get_global_id(0);
|
||||
unsigned int j;
|
||||
if(i >= n)
|
||||
return;
|
||||
// Evaluate the row
|
||||
Y[i] = 0.f;
|
||||
for(j=0;j<n;j++){
|
||||
Y[i] += A[j + i*n]*X[j];
|
||||
}
|
||||
}
|
||||
|
||||
/** Solve a linear system using Minimal residues iterative method.
|
||||
* @param A Linear system matrix.
|
||||
* @param r Residues vector.
|
||||
* @param x0 Solution of the previous iteration.
|
||||
* @param x Solution of the actual iteration.
|
||||
* @param Ar_r dot(dot(A,r), r).
|
||||
* @param Ar_Ar dot(dot(A,r), dot(A,r)).
|
||||
* @param n Linear system dimension.
|
||||
*/
|
||||
__kernel void minres(__global float* A,
|
||||
__global float* r,
|
||||
__global float* x0,
|
||||
__global float* x,
|
||||
float Ar_r,
|
||||
float Ar_Ar,
|
||||
unsigned int n)
|
||||
{
|
||||
// find position in global arrays
|
||||
unsigned int i = get_global_id(0);
|
||||
if(i >= n)
|
||||
return;
|
||||
// Evaluate the row
|
||||
x[i] = x0[i] + Ar_r / Ar_Ar * r[i];
|
||||
}
|
||||
|
||||
|
|
@ -49,9 +49,10 @@ class TaskPanel:
|
|||
head = item.text().toFloat()[0]
|
||||
w.append([A,T,phi,head])
|
||||
obj = App.ActiveDocument.addObject("Part::FeaturePython","ShipSimulation")
|
||||
sim = SimInstance.ShipSimulation(obj,
|
||||
[form.length.value(), form.beam.value(), form.n.value()],
|
||||
w)
|
||||
sim = SimInstance.ShipSimulation(obj,
|
||||
[form.fsL.value(), form.fsB.value(), form.fsNx.value(), form.fsNy.value()],
|
||||
w,
|
||||
form.error.value())
|
||||
SimInstance.ViewProviderShipSimulation(obj.ViewObject)
|
||||
return True
|
||||
|
||||
|
|
@ -80,21 +81,25 @@ class TaskPanel:
|
|||
pass
|
||||
|
||||
def setupUi(self):
|
||||
mw = self.getMainWindow()
|
||||
form = mw.findChild(QtGui.QWidget, "TaskPanel")
|
||||
form.length = form.findChild(QtGui.QDoubleSpinBox, "Length")
|
||||
form.beam = form.findChild(QtGui.QDoubleSpinBox, "Beam")
|
||||
form.n = form.findChild(QtGui.QSpinBox, "N")
|
||||
form.waves = form.findChild(QtGui.QTableWidget, "Waves")
|
||||
mw = self.getMainWindow()
|
||||
form = mw.findChild(QtGui.QWidget, "TaskPanel")
|
||||
form.fsL = form.findChild(QtGui.QDoubleSpinBox, "Length")
|
||||
form.fsB = form.findChild(QtGui.QDoubleSpinBox, "Beam")
|
||||
form.fsNx = form.findChild(QtGui.QSpinBox, "Nx")
|
||||
form.fsNy = form.findChild(QtGui.QSpinBox, "Ny")
|
||||
form.error = form.findChild(QtGui.QDoubleSpinBox, "Error")
|
||||
form.waves = form.findChild(QtGui.QTableWidget, "Waves")
|
||||
self.form = form
|
||||
# Initial values
|
||||
if self.initValues():
|
||||
return True
|
||||
self.retranslateUi()
|
||||
# Connect Signals and Slots
|
||||
QtCore.QObject.connect(form.length, QtCore.SIGNAL("valueChanged(double)"), self.onFS)
|
||||
QtCore.QObject.connect(form.beam, QtCore.SIGNAL("valueChanged(double)"), self.onFS)
|
||||
QtCore.QObject.connect(form.n, QtCore.SIGNAL("valueChanged(int)"), self.onFS)
|
||||
QtCore.QObject.connect(form.fsL, QtCore.SIGNAL("valueChanged(double)"), self.onFS)
|
||||
QtCore.QObject.connect(form.fsB, QtCore.SIGNAL("valueChanged(double)"), self.onFS)
|
||||
QtCore.QObject.connect(form.fsNx, QtCore.SIGNAL("valueChanged(int)"), self.onFS)
|
||||
QtCore.QObject.connect(form.fsNy, QtCore.SIGNAL("valueChanged(int)"), self.onFS)
|
||||
QtCore.QObject.connect(form.error, QtCore.SIGNAL("valueChanged(double)"), self.onError)
|
||||
QtCore.QObject.connect(form.waves,QtCore.SIGNAL("cellChanged(int,int)"),self.onWaves);
|
||||
|
||||
def getMainWindow(self):
|
||||
|
|
@ -120,14 +125,12 @@ class TaskPanel:
|
|||
None,QtGui.QApplication.UnicodeUTF8))
|
||||
self.form.findChild(QtGui.QGroupBox, "FSDataBox").setTitle(QtGui.QApplication.translate("shipsim_create","Free surface",
|
||||
None,QtGui.QApplication.UnicodeUTF8))
|
||||
self.form.findChild(QtGui.QLabel, "LengthLabel").setText(QtGui.QApplication.translate("shipsim_create","Length",
|
||||
None,QtGui.QApplication.UnicodeUTF8))
|
||||
self.form.findChild(QtGui.QLabel, "BeamLabel").setText(QtGui.QApplication.translate("shipsim_create","Breadth",
|
||||
None,QtGui.QApplication.UnicodeUTF8))
|
||||
self.form.findChild(QtGui.QLabel, "NLabel").setText(QtGui.QApplication.translate("shipsim_create","Number of points",
|
||||
None,QtGui.QApplication.UnicodeUTF8))
|
||||
self.form.findChild(QtGui.QGroupBox, "WavesDataBox").setTitle(QtGui.QApplication.translate("shipsim_create","Waves",
|
||||
None,QtGui.QApplication.UnicodeUTF8))
|
||||
self.form.findChild(QtGui.QGroupBox, "OtherBox").setTitle(QtGui.QApplication.translate("shipsim_create","Other",
|
||||
None,QtGui.QApplication.UnicodeUTF8))
|
||||
self.form.findChild(QtGui.QLabel, "ErrorLabel").setText(QtGui.QApplication.translate("shipsim_create","Relative error",
|
||||
None,QtGui.QApplication.UnicodeUTF8))
|
||||
labels = []
|
||||
labels.append(QtGui.QApplication.translate("shipsim_create","Amplitude",
|
||||
None,QtGui.QApplication.UnicodeUTF8) + " [m]")
|
||||
|
|
@ -138,6 +141,27 @@ class TaskPanel:
|
|||
labels.append(QtGui.QApplication.translate("shipsim_create","Heading",
|
||||
None,QtGui.QApplication.UnicodeUTF8) + " [deg]")
|
||||
self.form.waves.setHorizontalHeaderLabels(labels)
|
||||
# Set some tooltips
|
||||
tooltip = QtGui.QApplication.translate("shipsim_create","Free surface length on x direction",
|
||||
None,QtGui.QApplication.UnicodeUTF8)
|
||||
self.form.findChild(QtGui.QLabel, "LengthLabel").setToolTip(tooltip)
|
||||
self.form.findChild(QtGui.QDoubleSpinBox, "Length").setToolTip(tooltip)
|
||||
tooltip = QtGui.QApplication.translate("shipsim_create","Free surface length on y direction",
|
||||
None,QtGui.QApplication.UnicodeUTF8)
|
||||
self.form.findChild(QtGui.QLabel, "BeamLabel").setToolTip(tooltip)
|
||||
self.form.findChild(QtGui.QDoubleSpinBox, "Beam").setToolTip(tooltip)
|
||||
tooltip = QtGui.QApplication.translate("shipsim_create","Number of nodes on x direction. Take into acount the following considerations:\n1.\tNodes must have an aspect ratio as near to 1,0 as possible, so this values must\n\taccomplish approximately that Nx/Ny = L/B\n3.\tThe linear system matrix generated will be of dimensions NxN, where\n\tN = Nx*Ny\n\tSo be mindful with the values selected and computer capabilities.",
|
||||
None,QtGui.QApplication.UnicodeUTF8)
|
||||
self.form.findChild(QtGui.QLabel, "NxLabel").setToolTip(tooltip)
|
||||
self.form.findChild(QtGui.QSpinBox, "Nx").setToolTip(tooltip)
|
||||
tooltip = QtGui.QApplication.translate("shipsim_create","Number of nodes on y direction. Take into acount the following considerations:\n1.\tNodes must have an aspect ratio as near to 1,0 as possible, so this values must\n\taccomplish approximately that Nx/Ny = L/B\n3.\tThe linear system matrix generated will be of dimensions NxN, where\n\tN = Nx*Ny\n\tSo be mindful with the values selected and computer capabilities.",
|
||||
None,QtGui.QApplication.UnicodeUTF8)
|
||||
self.form.findChild(QtGui.QLabel, "NyLabel").setToolTip(tooltip)
|
||||
self.form.findChild(QtGui.QSpinBox, "Ny").setToolTip(tooltip)
|
||||
tooltip = QtGui.QApplication.translate("shipsim_create","Relation between the minimum value of the Green's function (fartest point) and the maximum one.\nThis variable set the number of times that the Free surface will be virtually repeated.\nLower values may imply too much repeated free surfaces with a significant cost.",
|
||||
None,QtGui.QApplication.UnicodeUTF8)
|
||||
self.form.findChild(QtGui.QLabel, "ErrorLabel").setToolTip(tooltip)
|
||||
self.form.findChild(QtGui.QDoubleSpinBox, "Error").setToolTip(tooltip)
|
||||
|
||||
def onFS(self, value):
|
||||
""" Method called when free surface data is changed.
|
||||
|
|
@ -145,6 +169,12 @@ class TaskPanel:
|
|||
"""
|
||||
pass
|
||||
|
||||
def onError(self, value):
|
||||
""" Method called when sea data is changed.
|
||||
@param value Changed value.
|
||||
"""
|
||||
pass
|
||||
|
||||
def onWaves(self, row, column):
|
||||
""" Method called when waves data is changed.
|
||||
@param row Affected row.
|
||||
|
|
|
|||
|
|
@ -6,7 +6,7 @@
|
|||
<rect>
|
||||
<x>0</x>
|
||||
<y>0</y>
|
||||
<width>269</width>
|
||||
<width>386</width>
|
||||
<height>384</height>
|
||||
</rect>
|
||||
</property>
|
||||
|
|
@ -42,7 +42,7 @@
|
|||
<property name="minimumSize">
|
||||
<size>
|
||||
<width>0</width>
|
||||
<height>128</height>
|
||||
<height>0</height>
|
||||
</size>
|
||||
</property>
|
||||
<property name="title">
|
||||
|
|
@ -55,11 +55,11 @@
|
|||
<bool>false</bool>
|
||||
</property>
|
||||
<layout class="QVBoxLayout" name="verticalLayout_2">
|
||||
<property name="sizeConstraint">
|
||||
<enum>QLayout::SetDefaultConstraint</enum>
|
||||
</property>
|
||||
<item>
|
||||
<layout class="QHBoxLayout" name="horizontalLayout_2">
|
||||
<property name="spacing">
|
||||
<number>2</number>
|
||||
</property>
|
||||
<property name="sizeConstraint">
|
||||
<enum>QLayout::SetMinimumSize</enum>
|
||||
</property>
|
||||
|
|
@ -78,15 +78,27 @@
|
|||
<item>
|
||||
<widget class="QLabel" name="LengthLabel">
|
||||
<property name="text">
|
||||
<string>Length</string>
|
||||
<string>L</string>
|
||||
</property>
|
||||
</widget>
|
||||
</item>
|
||||
<item>
|
||||
<widget class="QDoubleSpinBox" name="Length">
|
||||
<property name="sizePolicy">
|
||||
<sizepolicy hsizetype="Expanding" vsizetype="Fixed">
|
||||
<horstretch>0</horstretch>
|
||||
<verstretch>0</verstretch>
|
||||
</sizepolicy>
|
||||
</property>
|
||||
<property name="alignment">
|
||||
<set>Qt::AlignRight|Qt::AlignTrailing|Qt::AlignVCenter</set>
|
||||
</property>
|
||||
<property name="decimals">
|
||||
<number>1</number>
|
||||
</property>
|
||||
<property name="minimum">
|
||||
<double>1.000000000000000</double>
|
||||
</property>
|
||||
<property name="maximum">
|
||||
<double>1000000.000000000000000</double>
|
||||
</property>
|
||||
|
|
@ -98,37 +110,30 @@
|
|||
</property>
|
||||
</widget>
|
||||
</item>
|
||||
</layout>
|
||||
</item>
|
||||
<item>
|
||||
<layout class="QHBoxLayout" name="horizontalLayout_4">
|
||||
<property name="sizeConstraint">
|
||||
<enum>QLayout::SetMinimumSize</enum>
|
||||
</property>
|
||||
<property name="leftMargin">
|
||||
<number>10</number>
|
||||
</property>
|
||||
<property name="topMargin">
|
||||
<number>0</number>
|
||||
</property>
|
||||
<property name="rightMargin">
|
||||
<number>10</number>
|
||||
</property>
|
||||
<property name="bottomMargin">
|
||||
<number>0</number>
|
||||
</property>
|
||||
<item>
|
||||
<widget class="QLabel" name="BeamLabel">
|
||||
<property name="text">
|
||||
<string>Beam</string>
|
||||
<string>B</string>
|
||||
</property>
|
||||
</widget>
|
||||
</item>
|
||||
<item>
|
||||
<widget class="QDoubleSpinBox" name="Beam">
|
||||
<property name="sizePolicy">
|
||||
<sizepolicy hsizetype="Expanding" vsizetype="Fixed">
|
||||
<horstretch>0</horstretch>
|
||||
<verstretch>0</verstretch>
|
||||
</sizepolicy>
|
||||
</property>
|
||||
<property name="alignment">
|
||||
<set>Qt::AlignRight|Qt::AlignTrailing|Qt::AlignVCenter</set>
|
||||
</property>
|
||||
<property name="decimals">
|
||||
<number>1</number>
|
||||
</property>
|
||||
<property name="minimum">
|
||||
<double>1.000000000000000</double>
|
||||
</property>
|
||||
<property name="maximum">
|
||||
<double>1000000.000000000000000</double>
|
||||
</property>
|
||||
|
|
@ -160,22 +165,60 @@
|
|||
<number>0</number>
|
||||
</property>
|
||||
<item>
|
||||
<widget class="QLabel" name="NLabel">
|
||||
<widget class="QLabel" name="NxLabel">
|
||||
<property name="text">
|
||||
<string>Number of points</string>
|
||||
<string>Nx</string>
|
||||
</property>
|
||||
</widget>
|
||||
</item>
|
||||
<item>
|
||||
<widget class="QSpinBox" name="N">
|
||||
<widget class="QSpinBox" name="Nx">
|
||||
<property name="sizePolicy">
|
||||
<sizepolicy hsizetype="Expanding" vsizetype="Fixed">
|
||||
<horstretch>0</horstretch>
|
||||
<verstretch>0</verstretch>
|
||||
</sizepolicy>
|
||||
</property>
|
||||
<property name="alignment">
|
||||
<set>Qt::AlignRight|Qt::AlignTrailing|Qt::AlignVCenter</set>
|
||||
</property>
|
||||
<property name="minimum">
|
||||
<number>3</number>
|
||||
</property>
|
||||
<property name="maximum">
|
||||
<number>10000000</number>
|
||||
</property>
|
||||
<property name="value">
|
||||
<number>25</number>
|
||||
</property>
|
||||
</widget>
|
||||
</item>
|
||||
<item>
|
||||
<widget class="QLabel" name="NyLabel">
|
||||
<property name="text">
|
||||
<string>Ny</string>
|
||||
</property>
|
||||
</widget>
|
||||
</item>
|
||||
<item>
|
||||
<widget class="QSpinBox" name="Ny">
|
||||
<property name="sizePolicy">
|
||||
<sizepolicy hsizetype="Expanding" vsizetype="Fixed">
|
||||
<horstretch>0</horstretch>
|
||||
<verstretch>0</verstretch>
|
||||
</sizepolicy>
|
||||
</property>
|
||||
<property name="alignment">
|
||||
<set>Qt::AlignRight|Qt::AlignTrailing|Qt::AlignVCenter</set>
|
||||
</property>
|
||||
<property name="minimum">
|
||||
<number>1</number>
|
||||
</property>
|
||||
<property name="maximum">
|
||||
<number>1000000000</number>
|
||||
<number>1000000</number>
|
||||
</property>
|
||||
<property name="value">
|
||||
<number>1000</number>
|
||||
<number>25</number>
|
||||
</property>
|
||||
</widget>
|
||||
</item>
|
||||
|
|
@ -260,6 +303,48 @@
|
|||
</layout>
|
||||
</widget>
|
||||
</item>
|
||||
<item>
|
||||
<widget class="QGroupBox" name="OtherBox">
|
||||
<property name="title">
|
||||
<string>Other</string>
|
||||
</property>
|
||||
<layout class="QVBoxLayout" name="verticalLayout_4">
|
||||
<item>
|
||||
<layout class="QHBoxLayout" name="horizontalLayout_3">
|
||||
<item>
|
||||
<widget class="QLabel" name="ErrorLabel">
|
||||
<property name="text">
|
||||
<string>Relative error</string>
|
||||
</property>
|
||||
</widget>
|
||||
</item>
|
||||
<item>
|
||||
<widget class="QDoubleSpinBox" name="Error">
|
||||
<property name="alignment">
|
||||
<set>Qt::AlignRight|Qt::AlignTrailing|Qt::AlignVCenter</set>
|
||||
</property>
|
||||
<property name="decimals">
|
||||
<number>4</number>
|
||||
</property>
|
||||
<property name="minimum">
|
||||
<double>0.000100000000000</double>
|
||||
</property>
|
||||
<property name="maximum">
|
||||
<double>1.000000000000000</double>
|
||||
</property>
|
||||
<property name="singleStep">
|
||||
<double>0.001000000000000</double>
|
||||
</property>
|
||||
<property name="value">
|
||||
<double>0.001000000000000</double>
|
||||
</property>
|
||||
</widget>
|
||||
</item>
|
||||
</layout>
|
||||
</item>
|
||||
</layout>
|
||||
</widget>
|
||||
</item>
|
||||
</layout>
|
||||
</item>
|
||||
</layout>
|
||||
|
|
|
|||
55
src/Mod/Ship/simRun/Sim/BEMsolver.py
Normal file
55
src/Mod/Ship/simRun/Sim/BEMsolver.py
Normal file
|
|
@ -0,0 +1,55 @@
|
|||
#***************************************************************************
|
||||
#* *
|
||||
#* Copyright (c) 2011, 2012 *
|
||||
#* Jose Luis Cercos Pita <jlcercos@gmail.com> *
|
||||
#* *
|
||||
#* This program is free software; you can redistribute it and/or modify *
|
||||
#* it under the terms of the GNU Lesser General Public License (LGPL) *
|
||||
#* as published by the Free Software Foundation; either version 2 of *
|
||||
#* the License, or (at your option) any later version. *
|
||||
#* for detail see the LICENCE text file. *
|
||||
#* *
|
||||
#* This program is distributed in the hope that it will be useful, *
|
||||
#* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||
#* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
|
||||
#* GNU Library General Public License for more details. *
|
||||
#* *
|
||||
#* You should have received a copy of the GNU Library General Public *
|
||||
#* License along with this program; if not, write to the Free Software *
|
||||
#* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 *
|
||||
#* USA *
|
||||
#* *
|
||||
#***************************************************************************
|
||||
|
||||
# numpy
|
||||
import numpy as np
|
||||
import scipy.linalg as la
|
||||
import FreeCAD
|
||||
|
||||
grav=9.81
|
||||
|
||||
class simBEMSolver:
|
||||
def __init__(self, context=None, queue=None):
|
||||
""" Constructor.
|
||||
@param context OpenCL context where apply. Only for compatibility,
|
||||
must be None.
|
||||
@param queue OpenCL command queue. Only for compatibility,
|
||||
must be None.
|
||||
"""
|
||||
self.context = context
|
||||
self.queue = queue
|
||||
|
||||
def execute(self, bem):
|
||||
""" Compute potential unknow data (gradients for free surface, and
|
||||
potentials for the other ones).
|
||||
@param bem Boundary Element Method instance.
|
||||
"""
|
||||
[bem['Ap'], residues, rank, s] = la.lstsq(bem['A'], bem['B'])
|
||||
if(rank < bem['N']):
|
||||
FreeCAD.Console.PrintError("\t\t[Sim]: Solving velocity potentials.\n")
|
||||
FreeCAD.Console.PrintError("\t\t\tEffective rank of linear system matrix is %i (N = %i)\n" % (rank, bem['N']))
|
||||
[bem['Adp'], residues, rank, s] = la.lstsq(bem['A'], bem['dB'])
|
||||
if(rank < bem['N']):
|
||||
FreeCAD.Console.PrintError("\t\t[Sim]: Solving acceleration potentials.\n")
|
||||
FreeCAD.Console.PrintError("\t\t\tEffective rank of linear system matrix is %i (N = %i)\n" % (rank, bem['N']))
|
||||
|
||||
|
|
@ -23,5 +23,5 @@
|
|||
|
||||
from initialization import *
|
||||
from matrixGen import *
|
||||
from computeSources import *
|
||||
from fsEvolution import *
|
||||
from BEMsolver import *
|
||||
from evolution import *
|
||||
|
|
|
|||
304
src/Mod/Ship/simRun/Sim/evolution.py
Normal file
304
src/Mod/Ship/simRun/Sim/evolution.py
Normal file
|
|
@ -0,0 +1,304 @@
|
|||
#***************************************************************************
|
||||
#* *
|
||||
#* Copyright (c) 2011, 2012 *
|
||||
#* Jose Luis Cercos Pita <jlcercos@gmail.com> *
|
||||
#* *
|
||||
#* This program is free software; you can redistribute it and/or modify *
|
||||
#* it under the terms of the GNU Lesser General Public License (LGPL) *
|
||||
#* as published by the Free Software Foundation; either version 2 of *
|
||||
#* the License, or (at your option) any later version. *
|
||||
#* for detail see the LICENCE text file. *
|
||||
#* *
|
||||
#* This program is distributed in the hope that it will be useful, *
|
||||
#* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||
#* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
|
||||
#* GNU Library General Public License for more details. *
|
||||
#* *
|
||||
#* You should have received a copy of the GNU Library General Public *
|
||||
#* License along with this program; if not, write to the Free Software *
|
||||
#* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 *
|
||||
#* USA *
|
||||
#* *
|
||||
#***************************************************************************
|
||||
|
||||
# numpy
|
||||
import numpy as np
|
||||
|
||||
grav=9.81
|
||||
|
||||
class simEvolution:
|
||||
def __init__(self, context=None, queue=None):
|
||||
""" Constructor.
|
||||
@param context OpenCL context where apply. Only for compatibility,
|
||||
must be None.
|
||||
@param queue OpenCL command queue. Only for compatibility,
|
||||
must be None.
|
||||
"""
|
||||
self.context = context
|
||||
self.queue = queue
|
||||
|
||||
def executeRK4(self, x, dx, p, dp, pos, vel, phi, dphi, fs, sea, body, waves, dt, t, stage):
|
||||
""" Compute free surface RK4 stage evolution process (valid for stages 1,2 and 3).
|
||||
@param x Output free surface z coordinates.
|
||||
@param dx Output free surface z coordinates variation (dz/dt).
|
||||
@param p Output potentials.
|
||||
@param dp Output potentials variation (dphi/dt).
|
||||
@param pos Input free surface positions.
|
||||
@param vel Input free surface velocities.
|
||||
@param phi Input potentials.
|
||||
@param dphi Input potentials variation (dphi/dt).
|
||||
@param fs Free surface instance.
|
||||
@param sea Sea instance.
|
||||
@param body Body instance.
|
||||
@param waves Waves instance.
|
||||
@param dt Time step.
|
||||
@param t Actual time (without adding dt).
|
||||
@param stage Runge-Kutta4 stage.
|
||||
@return Input variables evoluted one time step.
|
||||
"""
|
||||
# --------------------------------------------
|
||||
# Only free surface
|
||||
# --------------------------------------------
|
||||
h = fs['h']
|
||||
nx = fs['Nx']
|
||||
ny = fs['Ny']
|
||||
nF = nx*ny
|
||||
factor = 0.5
|
||||
if stage > 2:
|
||||
factor = 1.
|
||||
for i in range(0,nx):
|
||||
for j in range(0,ny):
|
||||
x[i,j] = np.copy(pos[i,j][2])
|
||||
dx[i,j] = np.copy(vel[i,j][2])
|
||||
x[i,j] = x[i,j] + factor*dt*dx[i,j]
|
||||
p[i*ny+j] = np.copy(phi[i*ny+j])
|
||||
dp[i*ny+j] = np.copy(dphi[i*ny+j])
|
||||
p[i*ny+j] = p[i*ny+j] + factor*dt*dp[i*ny+j]
|
||||
# Impose values at beach (far free surface)
|
||||
nbx = fs['Beachx']
|
||||
nby = fs['Beachy']
|
||||
for i in range(0,nx):
|
||||
for j in range(0,nby) + range(ny-nby,ny):
|
||||
[x[i,j],dx[i,j],p[i*ny+j],dp[i*ny+j]] = self.beach(pos[i,j], waves, factor*dt, t)
|
||||
for j in range(0,ny):
|
||||
for i in range(0,nbx) + range(nx-nbx,nx):
|
||||
[x[i,j],dx[i,j],p[i*ny+j],dp[i*ny+j]] = self.beach(pos[i,j], waves, factor*dt, t)
|
||||
# --------------------------------------------
|
||||
# Sea boundaries, where potentials are fixed.
|
||||
# We use the gradient projected over normal,
|
||||
# see initialization for more details about
|
||||
# this.
|
||||
# --------------------------------------------
|
||||
ids = ['front','back','left','right','bottom']
|
||||
i0 = fs['N']
|
||||
for index in ids:
|
||||
s = sea[index]
|
||||
nx = s['Nx']
|
||||
ny = s['Ny']
|
||||
for i in range(0,nx):
|
||||
for j in range(0,ny):
|
||||
p[i0 + i*ny+j] = 0.
|
||||
dp[i0 + i*ny+j] = 0.
|
||||
for w in waves['data']:
|
||||
A = w[0]
|
||||
T = w[1]
|
||||
phase = w[2]
|
||||
heading = np.pi*w[3]/180.0
|
||||
wl = 0.5 * grav / np.pi * T*T
|
||||
k = 2.0*np.pi/wl
|
||||
frec = 2.0*np.pi/T
|
||||
pos = s['pos'][i,j]
|
||||
l = pos[0]*np.cos(heading) + pos[1]*np.sin(heading)
|
||||
normal = s['normal'][i,j]
|
||||
hfact = np.cosh(k*(pos[2]+h)) / np.cosh(k*h)
|
||||
factor = np.dot(normal,np.array([np.cos(heading), np.sin(heading), 0.]))
|
||||
amp = frec*A*np.sin(k*l - frec*(t+factor*dt) + phase)*hfact
|
||||
p[i0 + i*ny+j] = p[i0 + i*ny+j] + factor*amp
|
||||
amp = - grav*A*k*np.cos(k*l - frec*(t+factor*dt) + phase)*hfact
|
||||
dp[i0 + i*ny+j] = dp[i0 + i*ny+j] + factor*amp
|
||||
i0 = i0 + s['N']
|
||||
|
||||
def execute(self, dx1, dx2, dx3, dp1, dp2, dp3, fs, sea, body, waves, bem, dt, t):
|
||||
""" Compute free surface evolution process (execute it on RK4 last stage).
|
||||
@param dx1 Input free surface positions variation on stage 1.
|
||||
@param dx2 Input free surface positions variation on stage 2.
|
||||
@param dx3 Input free surface positions variation on stage 3.
|
||||
@param dp1 Input free surface potentials variation on stage 1.
|
||||
@param dp2 Input free surface potentials variation on stage 2.
|
||||
@param dp3 Input free surface potentials variation on stage 3.
|
||||
@param fs Free surface instance.
|
||||
@param sea Sea instance.
|
||||
@param body Body instance.
|
||||
@param waves Waves instance.
|
||||
@param bem Boundary Element Method instance.
|
||||
@param dt Time step.
|
||||
@param t Actual time (without adding dt).
|
||||
@param stage Runge-Kutta4 stage.
|
||||
@return Input variables evoluted one time step.
|
||||
"""
|
||||
h = fs['h']
|
||||
nx = fs['Nx']
|
||||
ny = fs['Ny']
|
||||
nF = nx*ny
|
||||
for i in range(0,nx):
|
||||
for j in range(0,ny):
|
||||
# In this stage dx4 and dp4 are directly known from the previous
|
||||
# stage.
|
||||
dx4 = fs['vel'][i,j][2]
|
||||
dp4 = bem['dp4'][i*ny+j]
|
||||
# And we only need to apply the integration scheme
|
||||
fs['pos'][i,j][2] = fs['pos'][i,j][2] + dt/6. * (dx1[i,j] + 2.*dx2[i,j] + 2.*dx3[i,j] + dx4)
|
||||
bem['p4'][i*ny+j] = bem['p4'][i*ny+j] + dt/6. * (dp1[i*ny+j] + 2.*dp2[i*ny+j] + 2.*dp3[i*ny+j] + dp4)
|
||||
# In order to can apply the boundary condition at the free surface
|
||||
# at the end of this RK4 stage, we need to store eta in a variable.
|
||||
# x1 is safe because will be over written at the start of next
|
||||
# time step.
|
||||
fs['x1'][i,j] = fs['pos'][i,j][2]
|
||||
# Impose values at beach (far free surface)
|
||||
nbx = fs['Beachx']
|
||||
nby = fs['Beachy']
|
||||
for i in range(0,nx):
|
||||
for j in range(0,nby) + range(ny-nby,ny):
|
||||
[x,dummy,p,dummy] = self.beach(fs['pos'][i,j], waves, dt, t)
|
||||
fs['pos'][i,j][2] = x
|
||||
bem['p4'][i*ny+j] = p
|
||||
fs['x1'][i,j] = fs['pos'][i,j][2]
|
||||
for j in range(0,ny):
|
||||
for i in range(0,nbx) + range(nx-nbx,nx):
|
||||
[x,dummy,p,dummy] = self.beach(fs['pos'][i,j], waves, dt, t)
|
||||
fs['pos'][i,j][2] = x
|
||||
bem['p4'][i*ny+j] = p
|
||||
fs['x1'][i,j] = fs['pos'][i,j][2]
|
||||
# --------------------------------------------
|
||||
# Sea boundaries, where potentials are fixed.
|
||||
# We use the gradient projected over normal,
|
||||
# see initialization for more details about
|
||||
# this.
|
||||
# --------------------------------------------
|
||||
ids = ['front','back','left','right','bottom']
|
||||
i0 = fs['N']
|
||||
p = bem['p4']
|
||||
dp = bem['dp4']
|
||||
for index in ids:
|
||||
s = sea[index]
|
||||
nx = s['Nx']
|
||||
ny = s['Ny']
|
||||
for i in range(0,nx):
|
||||
for j in range(0,ny):
|
||||
p[i0 + i*ny+j] = 0.
|
||||
dp[i0 + i*ny+j] = 0.
|
||||
for w in waves['data']:
|
||||
A = w[0]
|
||||
T = w[1]
|
||||
phase = w[2]
|
||||
heading = np.pi*w[3]/180.0
|
||||
wl = 0.5 * grav / np.pi * T*T
|
||||
k = 2.0*np.pi/wl
|
||||
frec = 2.0*np.pi/T
|
||||
pos = s['pos'][i,j]
|
||||
l = pos[0]*np.cos(heading) + pos[1]*np.sin(heading)
|
||||
normal = s['normal'][i,j]
|
||||
hfact = np.cosh(k*(pos[2]+h)) / np.cosh(k*h)
|
||||
factor = np.dot(normal,np.array([np.cos(heading), np.sin(heading), 0.]))
|
||||
amp = frec*A*np.sin(k*l - frec*(t+factor*dt) + phase)*hfact
|
||||
p[i0 + i*ny+j] = p[i0 + i*ny+j] + factor*amp
|
||||
amp = - grav*A*k*np.cos(k*l - frec*(t+factor*dt) + phase)*hfact
|
||||
dp[i0 + i*ny+j] = dp[i0 + i*ny+j] + factor*amp
|
||||
i0 = i0 + s['N']
|
||||
|
||||
def executeFSBC(self, x, fs, sea, body, waves, bem, dt, t, stage):
|
||||
""" Compute free surface boundary conditions in order to get
|
||||
free surface points velocity and potentials acceleration for
|
||||
the next RK4 stage.
|
||||
@param x Free surface z coordinates.
|
||||
@param fs Free surface instance.
|
||||
@param sea Sea boundaries instance.
|
||||
@param body Body instance.
|
||||
@param waves Waves instance.
|
||||
@param bem Boundary Element Method instance.
|
||||
@param dt Time step.
|
||||
@param t Actual time (without adding dt).
|
||||
"""
|
||||
nx = fs['Nx']
|
||||
ny = fs['Ny']
|
||||
nF = nx*ny
|
||||
factor = 0.5
|
||||
if stage > 2:
|
||||
factor = 1.
|
||||
for i in range(0,nx):
|
||||
for j in range(0,ny):
|
||||
pos = np.copy(fs['pos'][i,j])
|
||||
pos[2] = x[i,j]
|
||||
gradVal = bem['Ap'][i*ny+j]
|
||||
normal = fs['normal'][i,j]
|
||||
# v_z = dphi/dz - grad(phi)*grad(z) - U*dz/dx
|
||||
dzdt = gradVal*normal[2]
|
||||
# dphi/dt = - rho*g*z - 0.5*grad(phi)^2 + v_z*dphi/dz - p_0 - U*dphi/dx - dU/dt*x
|
||||
dphidt = -grav*pos[2] - 0.5*np.dot(gradVal,gradVal) # + dzdt*gradVal*normal[2]
|
||||
# We need to preserve data on free surface global
|
||||
# velocity and potential values in order to use as
|
||||
# input of the next RK4 stage
|
||||
fs['vel'][i,j][2] = dzdt
|
||||
bem['dp4'][i*ny+j] = dphidt
|
||||
# Impose values at beach (far free surface)
|
||||
nbx = fs['Beachx']
|
||||
nby = fs['Beachy']
|
||||
for i in range(0,nx):
|
||||
for j in range(0,nby) + range(ny-nby,ny):
|
||||
[dummy,dx,dummy,dp] = self.beach(fs['pos'][i,j], waves, factor*dt, t)
|
||||
fs['vel'][i,j][2] = dx
|
||||
bem['dp4'][i*ny+j] = dp
|
||||
for j in range(0,ny):
|
||||
for i in range(0,nbx) + range(nx-nbx,nx):
|
||||
[dummy,dx,dummy,dp] = self.beach(fs['pos'][i,j], waves, factor*dt, t)
|
||||
fs['vel'][i,j][2] = dx
|
||||
bem['dp4'][i*ny+j] = dp
|
||||
|
||||
def beach(self, pos, waves, dt, t):
|
||||
""" Compute far free surface where only
|
||||
incident waves can be taken into account.
|
||||
@param pos Free surface position.
|
||||
@param waves Waves instance.
|
||||
@param dt Time step.
|
||||
@param t Actual time (without adding dt).
|
||||
@return Position, velocity, potential and potential acceleration
|
||||
"""
|
||||
h = waves['h']
|
||||
x = 0.
|
||||
dx = 0.
|
||||
p = 0.
|
||||
dp = 0.
|
||||
# Since values of the potencial, and this acceleration,
|
||||
# depends on z, we need to compute first the positions.
|
||||
for w in waves['data']:
|
||||
A = w[0]
|
||||
T = w[1]
|
||||
phase = w[2]
|
||||
heading = np.pi*w[3]/180.0
|
||||
wl = 0.5 * grav / np.pi * T*T
|
||||
k = 2.0*np.pi/wl
|
||||
frec = 2.0*np.pi/T
|
||||
l = pos[0]*np.cos(heading) + pos[1]*np.sin(heading)
|
||||
# hfact = np.sinh(k*(pos[2]+h)) / np.cosh(k*h)
|
||||
hfact = 1.0
|
||||
amp = A*np.sin(k*l - frec*(t+dt) + phase)*hfact
|
||||
x = x + amp
|
||||
amp = - A*frec*np.cos(k*l - frec*(t+dt) + phase)*hfact
|
||||
dx = dx + amp
|
||||
# And now we can compute potentials.
|
||||
for w in waves['data']:
|
||||
A = w[0]
|
||||
T = w[1]
|
||||
phase = w[2]
|
||||
heading = np.pi*w[3]/180.0
|
||||
wl = 0.5 * grav / np.pi * T*T
|
||||
k = 2.0*np.pi/wl
|
||||
frec = 2.0*np.pi/T
|
||||
l = pos[0]*np.cos(heading) + pos[1]*np.sin(heading)
|
||||
hfact = np.cosh(k*(x+h)) / np.cosh(k*h)
|
||||
amp = - grav/frec*A*np.sin(k*l - frec*(t+dt) + phase)*hfact
|
||||
p = p + amp
|
||||
amp = grav*A*np.cos(k*l - frec*(t+dt) + phase)*hfact
|
||||
dp = dp + amp
|
||||
return [x,dx,p,dp]
|
||||
|
||||
|
|
@ -1,119 +1,327 @@
|
|||
#***************************************************************************
|
||||
#* *
|
||||
#* Copyright (c) 2011, 2012 *
|
||||
#* Jose Luis Cercos Pita <jlcercos@gmail.com> *
|
||||
#* *
|
||||
#* *
|
||||
#* Copyright (c) 2011, 2012 *
|
||||
#* Jose Luis Cercos Pita <jlcercos@gmail.com> *
|
||||
#* *
|
||||
#* This program is free software; you can redistribute it and/or modify *
|
||||
#* it under the terms of the GNU Lesser General Public License (LGPL) *
|
||||
#* as published by the Free Software Foundation; either version 2 of *
|
||||
#* the License, or (at your option) any later version. *
|
||||
#* for detail see the LICENCE text file. *
|
||||
#* *
|
||||
#* This program is distributed in the hope that it will be useful, *
|
||||
#* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||
#* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
|
||||
#* GNU Library General Public License for more details. *
|
||||
#* *
|
||||
#* You should have received a copy of the GNU Library General Public *
|
||||
#* it under the terms of the GNU Lesser General Public License (LGPL) *
|
||||
#* as published by the Free Software Foundation; either version 2 of *
|
||||
#* the License, or (at your option) any later version. *
|
||||
#* for detail see the LICENCE text file. *
|
||||
#* *
|
||||
#* This program is distributed in the hope that it will be useful, *
|
||||
#* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||
#* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
|
||||
#* GNU Library General Public License for more details. *
|
||||
#* *
|
||||
#* You should have received a copy of the GNU Library General Public *
|
||||
#* License along with this program; if not, write to the Free Software *
|
||||
#* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 *
|
||||
#* USA *
|
||||
#* *
|
||||
#* USA *
|
||||
#* *
|
||||
#***************************************************************************
|
||||
|
||||
# numpy
|
||||
import numpy as np
|
||||
import FreeCAD
|
||||
|
||||
grav=9.81
|
||||
|
||||
class simInitialization:
|
||||
def __init__(self, FSmesh, waves, context=None, queue=None):
|
||||
""" Constructor.
|
||||
@param FSmesh Initial free surface mesh.
|
||||
@param waves Considered simulation waves (A,T,phi,heading).
|
||||
@param context OpenCL context where apply. Only for compatibility,
|
||||
must be None.
|
||||
@param queue OpenCL command queue. Only for compatibility,
|
||||
must be None.
|
||||
"""
|
||||
self.context = context
|
||||
self.queue = queue
|
||||
self.loadData(FSmesh, waves)
|
||||
self.execute()
|
||||
# Compute time step
|
||||
self.dt = 0.1
|
||||
for w in self.waves['data']:
|
||||
if(self.dt > w[1]/200.0):
|
||||
self.dt = w[1]/200.0
|
||||
def __init__(self, h, FSMesh, SeaMesh, waves, context=None, queue=None):
|
||||
""" Constructor.
|
||||
@param h Water height.
|
||||
@param FSMesh Initial free surface mesh.
|
||||
@param waves Considered simulation waves (A,T,phi,heading).
|
||||
@param context OpenCL context where apply. Only for compatibility,
|
||||
must be None.
|
||||
@param queue OpenCL command queue. Only for compatibility,
|
||||
must be None.
|
||||
"""
|
||||
self.context = context
|
||||
self.queue = queue
|
||||
self.loadData(h, FSMesh, SeaMesh, waves)
|
||||
self.execute()
|
||||
# Compute time step
|
||||
self.dt = 0.1
|
||||
for w in self.waves['data']:
|
||||
if(self.dt > w[1]/200.0):
|
||||
self.dt = w[1]/200.0
|
||||
|
||||
def loadData(self, FSmesh, waves):
|
||||
""" Convert data to numpy format.
|
||||
@param FSmesh Initial free surface mesh.
|
||||
@param waves Considered simulation waves (A,T,phi,heading).
|
||||
"""
|
||||
nx = len(FSmesh)
|
||||
ny = len(FSmesh[0])
|
||||
nW = len(waves)
|
||||
# Mesh data
|
||||
p = np.ndarray((nx,ny, 3), dtype=np.float32)
|
||||
n = np.ndarray((nx,ny, 3), dtype=np.float32)
|
||||
a = np.ndarray((nx,ny), dtype=np.float32)
|
||||
phi = np.ndarray((nx,ny), dtype=np.float32)
|
||||
Phi = np.ndarray((nx,ny), dtype=np.float32)
|
||||
s = np.ndarray((nx,ny), dtype=np.float32)
|
||||
ss = np.ndarray((nx,ny), dtype=np.float32)
|
||||
for i in range(0, nx):
|
||||
for j in range(0, ny):
|
||||
pos = FSmesh[i][j].pos
|
||||
normal = FSmesh[i][j].normal
|
||||
area = FSmesh[i][j].area
|
||||
p[i,j,0] = pos.x
|
||||
p[i,j,1] = pos.y
|
||||
p[i,j,2] = pos.z
|
||||
n[i,j,0] = normal.x
|
||||
n[i,j,1] = normal.y
|
||||
n[i,j,2] = normal.z
|
||||
a[i,j] = area
|
||||
phi[i,j] = 0.
|
||||
Phi[i,j] = 0.
|
||||
s[i,j] = 0.
|
||||
ss[i,j] = 0.
|
||||
self.fs = {'Nx':nx, 'Ny':ny, 'pos':p, 'normal':n, 'area':a, \
|
||||
'velPot':phi, 'accPot':Phi, 'velSrc':s, 'accSrc':ss}
|
||||
# Waves data
|
||||
w = np.ndarray((nW, 4), dtype=np.float32)
|
||||
for i in range(0,nW):
|
||||
w[i,0] = waves[i][0]
|
||||
w[i,1] = waves[i][1]
|
||||
w[i,2] = waves[i][2]
|
||||
w[i,3] = waves[i][3]
|
||||
self.waves = {'N':nW, 'data':w}
|
||||
# Linear system matrix
|
||||
nF = nx*ny
|
||||
nB = 0 # No body for the moment
|
||||
N = nx*ny + nB
|
||||
self.A = np.ndarray((N, N), dtype=np.float32)
|
||||
def loadData(self, h, FSMesh, SeaMesh, waves):
|
||||
""" Convert data to numpy format.
|
||||
@param FSMesh Initial free surface mesh.
|
||||
@param waves Considered simulation waves (A,T,phi,heading).
|
||||
"""
|
||||
# Data will classified in four groups:
|
||||
# Free surface:
|
||||
# Is a key part of the simulation, so is
|
||||
# separated from the rest of water involved
|
||||
# elements.
|
||||
# Sea:
|
||||
# BEM method required a closed domain, so
|
||||
# water floor and sides must be append, but
|
||||
# are not a key objective of the simulation.
|
||||
# Body:
|
||||
# Is the main objective of the simulation.
|
||||
# Waves:
|
||||
# Data that is append as boundary condition.
|
||||
# BEM:
|
||||
# Used to solve the BEM problem and evolution.
|
||||
|
||||
# --------------------------------------------
|
||||
# Free surface data
|
||||
# N, Nx, Ny = Number of points in each
|
||||
# direction
|
||||
# pos = Positions
|
||||
# vel = Velocities
|
||||
# n = Normals
|
||||
# area = Areas
|
||||
# --------------------------------------------
|
||||
nx = len(FSMesh)
|
||||
ny = len(FSMesh[0])
|
||||
p = np.ndarray((nx,ny, 3), dtype=np.float32)
|
||||
V = np.zeros((nx,ny, 3), dtype=np.float32)
|
||||
n = np.ndarray((nx,ny, 3), dtype=np.float32)
|
||||
a = np.ndarray((nx,ny), dtype=np.float32)
|
||||
x1 = np.zeros((nx,ny), dtype=np.float32)
|
||||
x2 = np.zeros((nx,ny), dtype=np.float32)
|
||||
x3 = np.zeros((nx,ny), dtype=np.float32)
|
||||
dx1 = np.zeros((nx,ny), dtype=np.float32)
|
||||
dx2 = np.zeros((nx,ny), dtype=np.float32)
|
||||
dx3 = np.zeros((nx,ny), dtype=np.float32)
|
||||
for i in range(0, nx):
|
||||
for j in range(0, ny):
|
||||
pos = FSMesh[i][j].pos
|
||||
normal = FSMesh[i][j].normal
|
||||
area = FSMesh[i][j].area
|
||||
p[i,j,0] = pos.x
|
||||
p[i,j,1] = pos.y
|
||||
p[i,j,2] = pos.z
|
||||
n[i,j,0] = normal.x
|
||||
n[i,j,1] = normal.y
|
||||
n[i,j,2] = normal.z
|
||||
a[i,j] = area
|
||||
self.fs = {'h': h, 'N':nx*ny, 'Nx':nx, 'Ny':ny, \
|
||||
'pos':p, 'vel':V, 'normal':n, 'area':a, \
|
||||
'x1':x1, 'x2':x2, 'x3':x3,\
|
||||
'dx1':dx1, 'dx2':dx2, 'dx3':dx3}
|
||||
# --------------------------------------------
|
||||
# Sea data (dictionary with components
|
||||
# ['front','back','left','right','bottom'])
|
||||
# N, Nx, Ny = Number of points in each
|
||||
# direction
|
||||
# pos = Positions
|
||||
# vel = Velocities
|
||||
# n = Normals
|
||||
# area = Areas
|
||||
# --------------------------------------------
|
||||
self.sea = {'ids':['front','back','left','right','bottom']}
|
||||
N = 0
|
||||
for index in self.sea['ids']:
|
||||
mesh = SeaMesh[index]
|
||||
nx = len(mesh)
|
||||
ny = len(mesh[0])
|
||||
p = np.ndarray((nx,ny, 3), dtype=np.float32)
|
||||
V = np.zeros((nx,ny, 3), dtype=np.float32)
|
||||
n = np.ndarray((nx,ny, 3), dtype=np.float32)
|
||||
a = np.ndarray((nx,ny), dtype=np.float32)
|
||||
for i in range(0, nx):
|
||||
for j in range(0, ny):
|
||||
pos = mesh[i][j].pos
|
||||
normal = mesh[i][j].normal
|
||||
area = mesh[i][j].area
|
||||
p[i,j,0] = pos.x
|
||||
p[i,j,1] = pos.y
|
||||
p[i,j,2] = pos.z
|
||||
n[i,j,0] = normal.x
|
||||
n[i,j,1] = normal.y
|
||||
n[i,j,2] = normal.z
|
||||
a[i,j] = area
|
||||
d = {'N':nx*ny, 'Nx':nx, 'Ny':ny, 'pos':p, 'vel':V, 'normal':n, 'area':a}
|
||||
self.sea[index] = d
|
||||
N = N + nx*ny
|
||||
self.sea['N'] = N
|
||||
self.sea['h'] = h
|
||||
# --------------------------------------------
|
||||
# Body data
|
||||
# N, Nx, Ny = Number of points in each
|
||||
# direction
|
||||
# pos = Positions
|
||||
# vel = Velocities
|
||||
# n = Normals
|
||||
# area = Areas
|
||||
# --------------------------------------------
|
||||
self.b = {'N':0, 'pos':None, 'vel':None, 'normal':None, 'area':None}
|
||||
# --------------------------------------------
|
||||
# Waves data
|
||||
# N = Number of waves
|
||||
# data = Waves data
|
||||
# --------------------------------------------
|
||||
nW = len(waves)
|
||||
w = np.ndarray((nW, 4), dtype=np.float32)
|
||||
for i in range(0,nW):
|
||||
w[i,0] = waves[i][0]
|
||||
w[i,1] = waves[i][1]
|
||||
w[i,2] = waves[i][2]
|
||||
w[i,3] = waves[i][3]
|
||||
self.waves = {'h':h, 'N':nW, 'data':w}
|
||||
# --------------------------------------------
|
||||
# BEM data
|
||||
# N = nFS + nSea + nB
|
||||
# A,B,dB = Linear system matrix and vectors
|
||||
# p1,... = Velocity potentials (phi) for
|
||||
# each RK4 step. In reallity are
|
||||
# the independent term of the
|
||||
# BEM linear system, so is the
|
||||
# potential for the free surface,
|
||||
# and the gradient projected over
|
||||
# the normal along all other terms.
|
||||
# dp1,... = Acceleration potentials
|
||||
# (dphi/dt) for each RK4 step.
|
||||
# In reallity are the
|
||||
# independent term of the BEM
|
||||
# linear system, so is the
|
||||
# potential for the free surface,
|
||||
# and the gradient projected over
|
||||
# the normal along all other terms.
|
||||
# Ap,Adp = BEM solution vectors, that
|
||||
# contains the potential gradients
|
||||
# on free surface, and the potential
|
||||
# along all toher surfaces.
|
||||
# --------------------------------------------
|
||||
nFS = self.fs['N']
|
||||
nSea = self.sea['N']
|
||||
nB = self.b['N']
|
||||
N = nFS + nSea + nB
|
||||
A = np.zeros((N, N), dtype=np.float32)
|
||||
B = np.zeros((N), dtype=np.float32)
|
||||
dB = np.zeros((N), dtype=np.float32)
|
||||
p1 = np.zeros((N), dtype=np.float32)
|
||||
p2 = np.zeros((N), dtype=np.float32)
|
||||
p3 = np.zeros((N), dtype=np.float32)
|
||||
p4 = np.zeros((N), dtype=np.float32)
|
||||
Ap = np.zeros((N), dtype=np.float32)
|
||||
dp1 = np.zeros((N), dtype=np.float32)
|
||||
dp2 = np.zeros((N), dtype=np.float32)
|
||||
dp3 = np.zeros((N), dtype=np.float32)
|
||||
dp4 = np.zeros((N), dtype=np.float32)
|
||||
Adp = np.zeros((N), dtype=np.float32)
|
||||
self.bem = {'N':N, 'A':A, 'B':B, 'dB':dB, \
|
||||
'p1':p1, 'p2':p2, 'p3':p3, 'p4':p4, 'Ap':Ap, \
|
||||
'dp1':dp1, 'dp2':dp2, 'dp3':dp3, 'dp4':dp4, 'Adp':Adp }
|
||||
|
||||
def execute(self):
|
||||
""" Compute initial conditions. """
|
||||
# --------------------------------------------
|
||||
# Free surface beach nodes.
|
||||
# Beach nodes are the nodes of the free
|
||||
# surface where the waves are imposed. All
|
||||
# the other nodes are computed allowing non
|
||||
# linear waves due to the ship interaction.
|
||||
# The beach will have enough dimension to
|
||||
# control at least half wave length
|
||||
# --------------------------------------------
|
||||
# Get maximum wave length
|
||||
wl = 0.0
|
||||
for w in self.waves['data']:
|
||||
T = w[1]
|
||||
wl = max(wl, 0.5 * grav / np.pi * T*T)
|
||||
# Get nodes dimensions
|
||||
nx = self.fs['Nx']
|
||||
ny = self.fs['Ny']
|
||||
lx = self.fs['pos'][nx-1,0][0] - self.fs['pos'][0,0][0]
|
||||
ly = self.fs['pos'][0,ny-1][1] - self.fs['pos'][0,0][1]
|
||||
dx = lx / nx
|
||||
dy = ly / ny
|
||||
# Get number of nodes involved
|
||||
wnx = max(1, int(round(0.5*wl / dx)))
|
||||
wny = max(1, int(round(0.5*wl / dy)))
|
||||
wnx = min(wnx, nx)
|
||||
wny = min(wny, ny)
|
||||
self.fs['Beachx'] = wnx
|
||||
self.fs['Beachy'] = wny
|
||||
# --------------------------------------------
|
||||
# Free surface initial condition.
|
||||
# Since RK4 scheme starts on the end of
|
||||
# previous step, we only write on last
|
||||
# stage value (p4 and dp4)
|
||||
# --------------------------------------------
|
||||
nx = self.fs['Nx']
|
||||
ny = self.fs['Ny']
|
||||
h = self.fs['h']
|
||||
for i in range(0,nx):
|
||||
for j in range(0,ny):
|
||||
# Since initial values of the potencial, and this acceleration,
|
||||
# depends on z, we need to compute first the positions.
|
||||
self.fs['pos'][i,j][2] = 0.
|
||||
for w in self.waves['data']:
|
||||
A = w[0]
|
||||
T = w[1]
|
||||
phase = w[2]
|
||||
heading = np.pi*w[3]/180.0
|
||||
wl = 0.5 * grav / np.pi * T*T
|
||||
k = 2.0*np.pi/wl
|
||||
frec = 2.0*np.pi/T
|
||||
pos = self.fs['pos'][i,j]
|
||||
l = pos[0]*np.cos(heading) + pos[1]*np.sin(heading)
|
||||
# hfact = np.sinh(k*(pos[2]+h)) / np.cosh(k*h)
|
||||
hfact = 1.0
|
||||
amp = A*np.sin(k*l + phase)*hfact
|
||||
self.fs['pos'][i,j][2] = self.fs['pos'][i,j][2] + amp
|
||||
amp = - A*frec*np.cos(k*l + phase)*hfact
|
||||
self.fs['vel'][i,j][2] = self.fs['vel'][i,j][2] + amp
|
||||
# And now we can compute potentials.
|
||||
for w in self.waves['data']:
|
||||
A = w[0]
|
||||
T = w[1]
|
||||
phase = w[2]
|
||||
heading = np.pi*w[3]/180.0
|
||||
wl = 0.5 * grav / np.pi * T*T
|
||||
k = 2.0*np.pi/wl
|
||||
frec = 2.0*np.pi/T
|
||||
pos = self.fs['pos'][i,j]
|
||||
l = pos[0]*np.cos(heading) + pos[1]*np.sin(heading)
|
||||
hfact = np.cosh(k*(pos[2]+h)) / np.cosh(k*h)
|
||||
amp = - grav/frec*A*np.cos(k*l + phase)*hfact
|
||||
self.bem['p4'][i*ny+j] = self.bem['p4'][i*ny+j] + amp
|
||||
amp = - grav*A*np.sin(k*l + phase)*hfact
|
||||
self.bem['dp4'][i*ny+j] = self.bem['dp4'][i*ny+j] + amp
|
||||
# --------------------------------------------
|
||||
# Sea initial condition on sides.
|
||||
# 1. Since RK4 scheme starts on the end of
|
||||
# previous step, we only write on last
|
||||
# stage value (p4 and dp4)
|
||||
# 2. In the sea boundaries we are
|
||||
# interested on the gradient of the
|
||||
# potentials projected over the normal,
|
||||
# so we really store this value.
|
||||
# 3. In the floor this value is ever null.
|
||||
# --------------------------------------------
|
||||
ids = ['front','back','left','right','bottom']
|
||||
i0 = self.fs['N']
|
||||
for index in ids:
|
||||
sea = self.sea[index]
|
||||
nx = sea['Nx']
|
||||
ny = sea['Ny']
|
||||
for i in range(0,nx):
|
||||
for j in range(0,ny):
|
||||
for w in self.waves['data']:
|
||||
A = w[0]
|
||||
T = w[1]
|
||||
phase = w[2]
|
||||
heading = np.pi*w[3]/180.0
|
||||
wl = 0.5 * grav / np.pi * T*T
|
||||
k = 2.0*np.pi/wl
|
||||
frec = 2.0*np.pi/T
|
||||
pos = sea['pos'][i,j]
|
||||
l = pos[0]*np.cos(heading) + pos[1]*np.sin(heading)
|
||||
normal = sea['normal'][i,j]
|
||||
hfact = np.cosh(k*(pos[2]+h)) / np.cosh(k*h)
|
||||
factor = np.dot(normal,np.array([np.cos(heading), np.sin(heading), 0.]))
|
||||
amp = frec*A*np.sin(k*l + phase)*hfact
|
||||
self.bem['p4'][i0 + i*ny+j] = self.bem['p4'][i*ny+j] + factor*amp
|
||||
amp = - grav*A*k*np.cos(k*l + phase)*hfact
|
||||
self.bem['dp4'][i0 + i*ny+j] = self.bem['dp4'][i*ny+j] + factor*amp
|
||||
i0 = i0 + sea['N']
|
||||
|
||||
def execute(self):
|
||||
""" Compute initial conditions. """
|
||||
nx = self.fs['Nx']
|
||||
ny = self.fs['Ny']
|
||||
for i in range(0,nx):
|
||||
for j in range(0,ny):
|
||||
self.fs['pos'][i,j][2] = 0.
|
||||
for w in self.waves['data']:
|
||||
A = w[0]
|
||||
T = w[1]
|
||||
phase = w[2]
|
||||
heading = np.pi*w[3]/180.0
|
||||
wl = 0.5 * grav / np.pi * T*T
|
||||
k = 2.0*np.pi/wl
|
||||
frec = 2.0*np.pi/T
|
||||
pos = self.fs['pos'][i,j]
|
||||
l = pos[0]*np.cos(heading) + pos[1]*np.sin(heading)
|
||||
amp = A*np.sin(k*l + phase)
|
||||
self.fs['pos'][i,j][2] = self.fs['pos'][i,j][2] + amp
|
||||
amp = - grav/frec*A*np.sin(k*l + phase)
|
||||
self.fs['velPot'][i,j] = self.fs['velPot'][i,j] + amp
|
||||
amp = grav*A*np.cos(k*l + phase)
|
||||
self.fs['accPot'][i,j] = self.fs['accPot'][i,j] + amp
|
||||
|
|
|
|||
|
|
@ -1,24 +1,24 @@
|
|||
#***************************************************************************
|
||||
#* *
|
||||
#* Copyright (c) 2011, 2012 *
|
||||
#* Jose Luis Cercos Pita <jlcercos@gmail.com> *
|
||||
#* *
|
||||
#* *
|
||||
#* Copyright (c) 2011, 2012 *
|
||||
#* Jose Luis Cercos Pita <jlcercos@gmail.com> *
|
||||
#* *
|
||||
#* This program is free software; you can redistribute it and/or modify *
|
||||
#* it under the terms of the GNU Lesser General Public License (LGPL) *
|
||||
#* as published by the Free Software Foundation; either version 2 of *
|
||||
#* the License, or (at your option) any later version. *
|
||||
#* for detail see the LICENCE text file. *
|
||||
#* *
|
||||
#* This program is distributed in the hope that it will be useful, *
|
||||
#* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||
#* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
|
||||
#* GNU Library General Public License for more details. *
|
||||
#* *
|
||||
#* You should have received a copy of the GNU Library General Public *
|
||||
#* it under the terms of the GNU Lesser General Public License (LGPL) *
|
||||
#* as published by the Free Software Foundation; either version 2 of *
|
||||
#* the License, or (at your option) any later version. *
|
||||
#* for detail see the LICENCE text file. *
|
||||
#* *
|
||||
#* This program is distributed in the hope that it will be useful, *
|
||||
#* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||
#* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
|
||||
#* GNU Library General Public License for more details. *
|
||||
#* *
|
||||
#* You should have received a copy of the GNU Library General Public *
|
||||
#* License along with this program; if not, write to the Free Software *
|
||||
#* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 *
|
||||
#* USA *
|
||||
#* *
|
||||
#* USA *
|
||||
#* *
|
||||
#***************************************************************************
|
||||
|
||||
# numpy
|
||||
|
|
@ -27,53 +27,197 @@ import numpy as np
|
|||
grav=9.81
|
||||
|
||||
class simMatrixGen:
|
||||
def __init__(self, context=None, queue=None):
|
||||
""" Constructor.
|
||||
@param context OpenCL context where apply. Only for compatibility,
|
||||
must be None.
|
||||
@param queue OpenCL command queue. Only for compatibility,
|
||||
must be None.
|
||||
"""
|
||||
self.context = context
|
||||
self.queue = queue
|
||||
def __init__(self, context=None, queue=None):
|
||||
""" Constructor.
|
||||
@param context OpenCL context where apply. Only for compatibility,
|
||||
must be None.
|
||||
@param queue OpenCL command queue. Only for compatibility,
|
||||
must be None.
|
||||
"""
|
||||
self.context = context
|
||||
self.queue = queue
|
||||
|
||||
def execute(self, fs, A):
|
||||
""" Compute system matrix.
|
||||
@param fs Free surface instance.
|
||||
@param A Linear system matrix.
|
||||
"""
|
||||
self.fs = fs
|
||||
nx = self.fs['Nx']
|
||||
ny = self.fs['Ny']
|
||||
nF = nx*ny
|
||||
nB = 0 # No body for the moment
|
||||
N = nx*ny + nB
|
||||
# Fluid sources rows
|
||||
for i in range(0,nx):
|
||||
for j in range(0,ny):
|
||||
# Append fluid effect
|
||||
pos = self.fs['pos'][i,j]
|
||||
A[i*ny+j,0:nF] = self.fluidEffect(pos)
|
||||
# Append body effect
|
||||
# ...
|
||||
def execute(self, x, p, dp, fs, sea, bem, body):
|
||||
""" Compute system matrix.
|
||||
@param x Free surface z coordinates.
|
||||
@param fs Free surface instance.
|
||||
@param sea Sea boundary instance.
|
||||
@param bem Boundary Element Method instance.
|
||||
@param body Body instance.
|
||||
"""
|
||||
nFS = fs['N']
|
||||
nSea = sea['N']
|
||||
nB = body['N']
|
||||
n = nFS + nSea + nB
|
||||
A = bem['A']
|
||||
B = bem['B']
|
||||
dB = bem['dB']
|
||||
# Free surface sources rows
|
||||
nx = fs['Nx']
|
||||
ny = fs['Ny']
|
||||
for i in range(0,nx):
|
||||
for j in range(0,ny):
|
||||
pos = np.copy(fs['pos'][i,j])
|
||||
pos[2] = x[i,j]
|
||||
# Compute G terms
|
||||
fsG = self.fsG(x, pos, fs)
|
||||
seaG = self.seaG(pos, sea)
|
||||
# Compute H terms
|
||||
fsH = self.fsH(i*ny+j, x, pos, fs)
|
||||
seaH = self.seaH(i*ny+j, pos, fs, sea)
|
||||
# Append terms to linear system matrix
|
||||
A[i*ny+j,0:nFS] = fsG
|
||||
A[i*ny+j,nFS:n] = seaH
|
||||
# Set independent terms
|
||||
B[i*ny+j] = np.dot(fsH, p[0:nFS]) + np.dot(seaG, p[nFS:nFS+nSea])
|
||||
dB[i*ny+j] = np.dot(fsH, dp[0:nFS]) + np.dot(seaG, dp[nFS:nFS+nSea])
|
||||
# Append body effect
|
||||
# ...
|
||||
# Sea sources rows
|
||||
ids = ['front','back','left','right','bottom']
|
||||
count = 0
|
||||
for index in ids:
|
||||
s = sea[index]
|
||||
nx = s['Nx']
|
||||
ny = s['Ny']
|
||||
for i in range(0,nx):
|
||||
for j in range(0,ny):
|
||||
pos = np.copy(s['pos'][i,j])
|
||||
# Compute G terms
|
||||
fsG = self.fsG(x, pos, fs)
|
||||
seaG = self.seaG(pos, sea)
|
||||
# Compute H terms
|
||||
fsH = self.fsH(nFS+count, x, pos, fs)
|
||||
seaH = self.seaH(nFS+count, pos, fs, sea)
|
||||
# Append terms to linear system matrix
|
||||
A[nFS+count, 0:nFS] = fsG
|
||||
A[nFS+count, nFS:n] = seaH
|
||||
# Set independent terms
|
||||
B[nFS+count] = np.dot(fsH, p[0:nFS]) + np.dot(seaG, p[nFS:nFS+nSea])
|
||||
dB[nFS+count] = np.dot(fsH, dp[0:nFS]) + np.dot(seaG, dp[nFS:nFS+nSea])
|
||||
# Append body effect
|
||||
# ...
|
||||
count = count + 1
|
||||
# Solid sources rows
|
||||
# ...
|
||||
|
||||
def fsG(self, x, pos, fs):
|
||||
r""" Compute free surface terms potential effect over desired position. Desingularized
|
||||
sources must taken into account.
|
||||
\$ G_{ij} = \sum_{j=0}^{n_{FS}-1} \log(\mathbf{r}_{ij}) \$
|
||||
@param x Free surface z coordinates.
|
||||
@param pos Point to evaluate.
|
||||
@param fs Free surface instance.
|
||||
@return Free surface effect row.
|
||||
"""
|
||||
nx = fs['Nx']
|
||||
ny = fs['Ny']
|
||||
nF = nx*ny
|
||||
row = np.ndarray(nF, dtype=np.float32)
|
||||
for i in range(0,nx):
|
||||
for j in range(0,ny):
|
||||
# Get source position (desingularized)
|
||||
source = np.copy(fs['pos'][i,j])
|
||||
source[2] = x[i,j]
|
||||
area = fs['area'][i,j]
|
||||
normal = fs['normal'][i,j]
|
||||
source = source + np.sqrt(area)*normal
|
||||
# Get union vector between points
|
||||
r = pos-source
|
||||
row[i*ny+j] = area * 0.5*np.log(np.dot(r,r))
|
||||
return row
|
||||
|
||||
def fsH(self, index, x, pos, fs):
|
||||
r""" Compute free surface terms potential gradient effect over desired position. Desingularized
|
||||
sources must taken into account.
|
||||
\$ H_{ij} = \sum_{j=0}^{n_{FS}-1} \frac{\mathbf{r}_{ij}}{\vert \mathbf{r}_{ij} \vert^2} \$
|
||||
When the point effect over himself is considered, -1/2 must be append.
|
||||
@param index Potential point index.
|
||||
@param x Free surface z coordinates.
|
||||
@param pos Point to evaluate.
|
||||
@param fs Free surface instance.
|
||||
@return Free surface effect row.
|
||||
"""
|
||||
nx = fs['Nx']
|
||||
ny = fs['Ny']
|
||||
nF = nx*ny
|
||||
row = np.ndarray(nF, dtype=np.float32)
|
||||
for i in range(0,nx):
|
||||
for j in range(0,ny):
|
||||
# Get source position (desingularized)
|
||||
source = np.copy(fs['pos'][i,j])
|
||||
source[2] = x[i,j]
|
||||
area = fs['area'][i,j]
|
||||
normal = fs['normal'][i,j]
|
||||
source = source + np.sqrt(area)*normal
|
||||
# Get union vector between points
|
||||
r = pos-source
|
||||
row[i*ny+j] = area * np.dot(r,normal) / np.dot(r,r)
|
||||
# If effect over himslef is considered, apply the correction
|
||||
if(index == i*ny+j):
|
||||
row[i*ny+j] = row[i*ny+j] - 0.5
|
||||
return row
|
||||
|
||||
def seaG(self, pos, sea):
|
||||
r""" Compute sea boundary terms potential effect over desired position. Desingularized
|
||||
sources must taken into account.
|
||||
\$ G_{ij} = \sum_{j=0}^{n_{FS}-1} \log(\mathbf{r}_{ij}) \$
|
||||
@param pos Point to evaluate.
|
||||
@param sea Sea boundaries instance.
|
||||
@return Sea boundaries effect row.
|
||||
"""
|
||||
ids = ['front','back','left','right','bottom']
|
||||
count = 0
|
||||
row = np.ndarray(sea['N'], dtype=np.float32)
|
||||
for index in ids:
|
||||
s = sea[index]
|
||||
nx = s['Nx']
|
||||
ny = s['Ny']
|
||||
for i in range(0,nx):
|
||||
for j in range(0,ny):
|
||||
# Get source position (desingularized)
|
||||
source = np.copy(s['pos'][i,j])
|
||||
area = s['area'][i,j]
|
||||
normal = s['normal'][i,j]
|
||||
source = source + np.sqrt(area)*normal
|
||||
# Get distance between points
|
||||
r = pos-source
|
||||
row[count] = area * 0.5*np.log(np.dot(r,r))
|
||||
count = count + 1
|
||||
return row
|
||||
|
||||
def seaH(self, index, pos, fs, sea):
|
||||
r""" Compute sea boundary terms potential gradient effect over desired position. Desingularized
|
||||
sources must taken into account.
|
||||
\$ H_{ij} = \sum_{j=0}^{n_{FS}-1} \frac{\mathbf{r}_{ij}}{\vert \mathbf{r}_{ij} \vert^2} \$
|
||||
When the point effect over himself is considered, -1/2 must be append.
|
||||
@param index Potential point index.
|
||||
@param pos Point to evaluate.
|
||||
@param fs Free surface instance.
|
||||
@param sea Sea boundaries instance.
|
||||
@return Sea boundaries effect row.
|
||||
"""
|
||||
nF = fs['N']
|
||||
ids = ['front','back','left','right','bottom']
|
||||
count = 0
|
||||
row = np.ndarray(sea['N'], dtype=np.float32)
|
||||
for index in ids:
|
||||
s = sea[index]
|
||||
nx = s['Nx']
|
||||
ny = s['Ny']
|
||||
for i in range(0,nx):
|
||||
for j in range(0,ny):
|
||||
# Get source position (desingularized)
|
||||
source = np.copy(s['pos'][i,j])
|
||||
area = s['area'][i,j]
|
||||
normal = s['normal'][i,j]
|
||||
source = source + np.sqrt(area)*normal
|
||||
# Get distance between points
|
||||
r = pos-source
|
||||
row[count] = area * np.dot(r,normal) / np.dot(r,r)
|
||||
# If effect over himslef is considered, apply the correction
|
||||
if(index == count+nF):
|
||||
row[count] = row[count] - 0.5
|
||||
count = count + 1
|
||||
return row
|
||||
|
||||
def fluidEffect(self, pos):
|
||||
""" Compute fluid effect terms over desired position. Desingularized
|
||||
sources must taken into account.
|
||||
@param pos Point to evaluate.
|
||||
@return Fluid effect row.
|
||||
"""
|
||||
nx = self.fs['Nx']
|
||||
ny = self.fs['Ny']
|
||||
nF = nx*ny
|
||||
row = np.ndarray(nF, dtype=np.float32)
|
||||
for i in range(0,nx):
|
||||
for j in range(0,ny):
|
||||
# Get source position (desingularized)
|
||||
source = np.copy(self.fs['pos'][i,j])
|
||||
area = self.fs['area'][i,j]
|
||||
source[2] = source[2] + np.sqrt(area)
|
||||
# Get distance between points
|
||||
d = np.linalg.norm(pos-source)
|
||||
row[i*ny+j] = np.log(d)*area
|
||||
return row
|
||||
|
|
@ -51,14 +51,17 @@ class Singleton(type):
|
|||
|
||||
class FreeCADShipSimulation(threading.Thread):
|
||||
__metaclass__ = Singleton
|
||||
def __init__ (self, device, endTime, output, simInstance, FSmesh, waves):
|
||||
def __init__ (self, device, endTime, output, simInstance, FSMesh, FSData, waves, Sea_Nx, Sea_Ny):
|
||||
""" Thread constructor.
|
||||
@param device Device to use.
|
||||
@param endTime Maximum simulation time.
|
||||
@param output [Rate,Type] Output rate, Type=0 if FPS, 1 if IPF.
|
||||
@param simInstance Simulaation instance.
|
||||
@param FSmesh Free surface mesh faces.
|
||||
@param FSMesh Free surface mesh faces.
|
||||
@param FSData Free surface data (Length, Breath, Nx, Ny).
|
||||
@param waves Waves parameters (A,T,phi,heading)
|
||||
@param Sea_Nx Times that the free surface is virtually repeated in the x direction
|
||||
@param Sea_Ny Times that the free surface is virtually repeated in the y direction
|
||||
"""
|
||||
threading.Thread.__init__(self)
|
||||
# Setup as stopped
|
||||
|
|
@ -75,9 +78,11 @@ class FreeCADShipSimulation(threading.Thread):
|
|||
self.endTime = endTime
|
||||
self.output = output
|
||||
self.sim = simInstance
|
||||
self.FSmesh = FSmesh
|
||||
self.FSMesh = FSMesh
|
||||
self.FSData = FSData
|
||||
self.waves = waves
|
||||
|
||||
self.Sea = (Sea_Nx, Sea_Ny)
|
||||
|
||||
def run(self):
|
||||
""" Runs the simulation.
|
||||
"""
|
||||
|
|
@ -90,36 +95,116 @@ class FreeCADShipSimulation(threading.Thread):
|
|||
msg = QtGui.QApplication.translate("ship_console","Initializating",
|
||||
None,QtGui.QApplication.UnicodeUTF8)
|
||||
FreeCAD.Console.PrintMessage("\t[Sim]: " + msg + "...\n")
|
||||
init = simInitialization(self.FSmesh,self.waves,self.context,self.queue)
|
||||
matGen = simMatrixGen(self.context,self.queue)
|
||||
solver = simComputeSources(self.context,self.queue)
|
||||
fsEvol = simFSEvolution(self.context,self.queue)
|
||||
A = init.A
|
||||
FS = init.fs
|
||||
waves = init.waves
|
||||
dt = init.dt
|
||||
if self.device == None: # Can't use OpenCL
|
||||
init = simInitialization(self.FSMesh,self.FSData,self.waves,self.Sea,self.context,self.queue)
|
||||
matGen = simMatrixGen(self.context,self.queue)
|
||||
solver = simBEMSolver(self.context,self.queue)
|
||||
evol = simEvolution(self.context,self.queue)
|
||||
else:
|
||||
init = simInitialization_cl(self.FSMesh,self.FSData,self.waves,self.Sea,self.context,self.queue)
|
||||
matGen = simMatrixGen_cl(self.context,self.queue)
|
||||
solver = simBEMSolver_cl(self.context,self.queue)
|
||||
evol = simEvolution_cl(self.context,self.queue)
|
||||
FS = init.fs
|
||||
sea = init.sea
|
||||
body = init.b
|
||||
waves = init.waves
|
||||
BEM = init.bem
|
||||
dt = init.dt
|
||||
self.t = 0.0
|
||||
self.FS = FS
|
||||
nx = FS['Nx']
|
||||
ny = FS['Ny']
|
||||
nx = FS['Nx']
|
||||
ny = FS['Ny']
|
||||
msg = QtGui.QApplication.translate("ship_console","Iterating",
|
||||
None,QtGui.QApplication.UnicodeUTF8)
|
||||
FreeCAD.Console.PrintMessage("\t[Sim]: " + msg + "...\n")
|
||||
while self.active and self.t < self.endTime:
|
||||
msg = QtGui.QApplication.translate("ship_console","Generating linear system matrix",
|
||||
None,QtGui.QApplication.UnicodeUTF8)
|
||||
FreeCAD.Console.PrintMessage("\t\t[Sim]: " + msg + "...\n")
|
||||
matGen.execute(FS, A)
|
||||
msg = QtGui.QApplication.translate("ship_console","Solving linear systems",
|
||||
None,QtGui.QApplication.UnicodeUTF8)
|
||||
FreeCAD.Console.PrintMessage("\t\t[Sim]: " + msg + "...\n")
|
||||
solver.execute(FS, A)
|
||||
msg = QtGui.QApplication.translate("ship_console","Time integrating",
|
||||
None,QtGui.QApplication.UnicodeUTF8)
|
||||
FreeCAD.Console.PrintMessage("\t\t[Sim]: " + msg + "...\n")
|
||||
fsEvol.execute(FS, waves, dt, self.t)
|
||||
# Simple Euler method
|
||||
FreeCAD.Console.PrintMessage("\t\t\t[Sim]: Generating matrix...\n")
|
||||
matGen.execute(FS, waves, sea, BEM, body, self.t)
|
||||
FreeCAD.Console.PrintMessage("\t\t\t[Sim]: Solving linear system matrix...\n")
|
||||
solver.execute(BEM)
|
||||
FreeCAD.Console.PrintMessage("\t\t\t[Sim]: Integrating...\n")
|
||||
# evol.execute(FS, BEM, waves, self.t, dt)
|
||||
|
||||
|
||||
# --------------------------------------------------------
|
||||
# Debugging
|
||||
# --------------------------------------------------------
|
||||
evol.BC(FS, BEM, waves, self.t)
|
||||
f = open("%.4f.dat" % (self.t), 'w')
|
||||
for i in range(0,FS['Nx']):
|
||||
for j in range(0, FS['Ny']):
|
||||
# Compute analitical solution
|
||||
z = 0.0
|
||||
vz = 0.0
|
||||
p = 0.0
|
||||
vp = 0.0
|
||||
for w in waves['data']:
|
||||
A = w[0]
|
||||
T = w[1]
|
||||
phase = w[2]
|
||||
heading = np.pi*w[3]/180.0
|
||||
wl = 0.5 * grav / np.pi * T*T
|
||||
k = 2.0*np.pi/wl
|
||||
frec = 2.0*np.pi/T
|
||||
pos = FS['pos'][i,j]
|
||||
l = pos[0]*np.cos(heading) + pos[1]*np.sin(heading)
|
||||
amp = A*np.sin(k*l - frec*self.t + phase)
|
||||
z = z + amp
|
||||
amp = - A*frec*np.cos(k*l - frec*self.t + phase)
|
||||
vz = vz + amp
|
||||
for w in waves['data']:
|
||||
A = w[0]
|
||||
T = w[1]
|
||||
phase = w[2]
|
||||
heading = np.pi*w[3]/180.0
|
||||
wl = 0.5 * grav / np.pi * T*T
|
||||
k = 2.0*np.pi/wl
|
||||
frec = 2.0*np.pi/T
|
||||
pos = FS['pos'][i,j]
|
||||
l = pos[0]*np.cos(heading) + pos[1]*np.sin(heading)
|
||||
amp = - A*frec/k*np.cos(k*l - frec*self.t + phase)*np.exp(k*z)
|
||||
p = p + amp
|
||||
amp = - A*9.81*np.sin(k*l - frec*self.t + phase)*np.exp(k*z)
|
||||
vp = vp + amp
|
||||
|
||||
"""
|
||||
z = 0.
|
||||
vz = 0.
|
||||
p = 0.
|
||||
vp = 0.
|
||||
# We can do phi = Green's function
|
||||
dx = FS['pos'][i,j][0]
|
||||
dy = FS['pos'][i,j][1]
|
||||
dz = 15.0 # An arbitrary value > 0
|
||||
p = 1. / (4. * np.pi * np.sqrt(dx*dx + dy*dy + dz*dz))
|
||||
vz = - dz / (4. * np.pi * (dx*dx + dy*dy + dz*dz)**(1.5))
|
||||
"""
|
||||
|
||||
# write coordinates
|
||||
f.write("%g %g " % (FS['pos'][i,j,0],FS['pos'][i,j,1]))
|
||||
# write computed wave and velocity
|
||||
f.write("%g %g " % (FS['pos'][i,j,2],FS['vel'][i,j,2]))
|
||||
# write computed potential and time variation rate
|
||||
# f.write("%g %g " % (BEM['p'][i*FS['Ny']+j],BEM['dpdt'][i*FS['Ny']+j]))
|
||||
f.write("%g %g " % (BEM['p'][i*FS['Ny']+j],0.))
|
||||
# write analytic wave and velocity
|
||||
f.write("%g %g " % (z,vz))
|
||||
# write analytic potential and time variation rate
|
||||
# f.write("%g %g\n" % (p,vp))
|
||||
f.write("%g %g\n" % (p,0.))
|
||||
f.write("\n")
|
||||
f.close()
|
||||
evol.Integrate(FS, BEM, waves, self.t, dt)
|
||||
# --------------------------------------------------------
|
||||
# Debugging
|
||||
# --------------------------------------------------------
|
||||
|
||||
|
||||
self.t = self.t + dt
|
||||
FreeCAD.Console.PrintMessage('\t[Sim]: t = %g s\n' % (self.t))
|
||||
|
||||
# Set thread as stopped (and prepare it to restarting)
|
||||
self.active = False
|
||||
threading.Event().set()
|
||||
|
|
|
|||
|
|
@ -61,18 +61,22 @@ class TaskPanel:
|
|||
device = d
|
||||
count = count + 1
|
||||
# Get free surfaces data
|
||||
FSMesh = SimInstance.FSMesh(self.sim)
|
||||
wData = self.sim.Waves
|
||||
wDir = self.sim.Waves_Dir
|
||||
waves = []
|
||||
FSMesh = SimInstance.FSMesh(self.sim)
|
||||
FSData = (self.sim.L,self.sim.B,self.sim.FS_Nx,self.sim.FS_Ny)
|
||||
wData = self.sim.Waves
|
||||
wDir = self.sim.Waves_Dir
|
||||
waves = []
|
||||
for i in range(0,len(wData)):
|
||||
waves.append([wData[i].x, wData[i].y, wData[i].z, wDir[i]])
|
||||
SeaNx = self.sim.Sea_Nx
|
||||
SeaNy = self.sim.Sea_Ny
|
||||
msg = QtGui.QApplication.translate("ship_console","Launching simulation",
|
||||
None,QtGui.QApplication.UnicodeUTF8)
|
||||
App.Console.PrintMessage(msg + "...\n")
|
||||
# Build simulation thread
|
||||
simulator = Sim(device, endTime, output, self.sim, FSMesh, waves)
|
||||
simulator.start()
|
||||
simulator = Sim(device, endTime, output, self.sim, FSMesh, FSData, waves, SeaNx, SeaNy)
|
||||
simulator.start() # Activate me for final release
|
||||
# simulator.run() # Activate me for development (i will show python fails)
|
||||
msg = QtGui.QApplication.translate("ship_console","Done",
|
||||
None,QtGui.QApplication.UnicodeUTF8)
|
||||
App.Console.PrintMessage(msg + "!\n")
|
||||
|
|
|
|||
61
src/Mod/Ship/simRun/clSim/BEMsolver.py
Normal file
61
src/Mod/Ship/simRun/clSim/BEMsolver.py
Normal file
|
|
@ -0,0 +1,61 @@
|
|||
#***************************************************************************
|
||||
#* *
|
||||
#* Copyright (c) 2011, 2012 *
|
||||
#* Jose Luis Cercos Pita <jlcercos@gmail.com> *
|
||||
#* *
|
||||
#* This program is free software; you can redistribute it and/or modify *
|
||||
#* it under the terms of the GNU Lesser General Public License (LGPL) *
|
||||
#* as published by the Free Software Foundation; either version 2 of *
|
||||
#* the License, or (at your option) any later version. *
|
||||
#* for detail see the LICENCE text file. *
|
||||
#* *
|
||||
#* This program is distributed in the hope that it will be useful, *
|
||||
#* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||
#* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
|
||||
#* GNU Library General Public License for more details. *
|
||||
#* *
|
||||
#* You should have received a copy of the GNU Library General Public *
|
||||
#* License along with this program; if not, write to the Free Software *
|
||||
#* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 *
|
||||
#* USA *
|
||||
#* *
|
||||
#***************************************************************************
|
||||
|
||||
# numpy
|
||||
import numpy as np
|
||||
from bem_jacobi_cl import jacobi
|
||||
from bem_minres_cl import minres
|
||||
from bem_lsqr_cl import lsqr
|
||||
import FreeCAD
|
||||
|
||||
grav=9.81
|
||||
|
||||
class simBEMSolver_cl:
|
||||
def __init__(self, context=None, queue=None):
|
||||
""" Constructor.
|
||||
@param context OpenCL context where apply.
|
||||
@param queue OpenCL command queue.
|
||||
"""
|
||||
self.context = context
|
||||
self.queue = queue
|
||||
self.solver = lsqr(context, queue)
|
||||
|
||||
def execute(self, bem):
|
||||
""" Compute potential unknow data (gradients for free surface, and
|
||||
potentials for the other ones).
|
||||
@param bem Boundary Element Method instance.
|
||||
"""
|
||||
"""
|
||||
[bem['gradp'], r, iters] = self.solver.solve(bem['A'], bem['B'], bem['gradp'])
|
||||
if(iters >= 300):
|
||||
FreeCAD.Console.PrintError("\t\t[Sim]: Solving velocity potentials.\n")
|
||||
FreeCAD.Console.PrintError("\t\t\tSolutions seems don't convergs after 300 iterations (%g residual)\n" % (r))
|
||||
FreeCAD.Console.PrintMessage((r,iters))
|
||||
FreeCAD.Console.PrintMessage("\n")
|
||||
"""
|
||||
import scipy.linalg as la
|
||||
[bem['gradp'], residues, rank, s] = la.lstsq(bem['A'], bem['B'])
|
||||
if(rank < bem['N']):
|
||||
FreeCAD.Console.PrintError("\t\t[Sim]: Solving velocity potentials.\n")
|
||||
FreeCAD.Console.PrintError("\t\t\tEffective rank of linear system matrix is {0} (N = {1})\n".format(rank, bem['N']))
|
||||
|
||||
|
|
@ -21,4 +21,7 @@
|
|||
#* *
|
||||
#***************************************************************************
|
||||
|
||||
import initialization, Utils
|
||||
from initialization import *
|
||||
from matrixGen import *
|
||||
from BEMsolver import *
|
||||
from evolution import *
|
||||
|
|
|
|||
155
src/Mod/Ship/simRun/clSim/bem_jacobi_cl.py
Normal file
155
src/Mod/Ship/simRun/clSim/bem_jacobi_cl.py
Normal file
|
|
@ -0,0 +1,155 @@
|
|||
#***************************************************************************
|
||||
#* *
|
||||
#* Copyright (c) 2011, 2012 *
|
||||
#* Jose Luis Cercos Pita <jlcercos@gmail.com> *
|
||||
#* *
|
||||
#* This program is free software; you can redistribute it and/or modify *
|
||||
#* it under the terms of the GNU Lesser General Public License (LGPL) *
|
||||
#* as published by the Free Software Foundation; either version 2 of *
|
||||
#* the License, or (at your option) any later version. *
|
||||
#* for detail see the LICENCE text file. *
|
||||
#* *
|
||||
#* This program is distributed in the hope that it will be useful, *
|
||||
#* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||
#* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
|
||||
#* GNU Library General Public License for more details. *
|
||||
#* *
|
||||
#* You should have received a copy of the GNU Library General Public *
|
||||
#* License along with this program; if not, write to the Free Software *
|
||||
#* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 *
|
||||
#* USA *
|
||||
#* *
|
||||
#***************************************************************************
|
||||
|
||||
# numpy
|
||||
import numpy as np
|
||||
|
||||
# pyOpenCL
|
||||
import pyopencl as cl
|
||||
from pyopencl.reduction import ReductionKernel
|
||||
import pyopencl.array as cl_array
|
||||
import clUtils
|
||||
|
||||
import FreeCAD
|
||||
grav=9.81
|
||||
|
||||
class jacobi:
|
||||
def __init__(self, context, queue):
|
||||
""" Constructor.
|
||||
@param context OpenCL context where apply.
|
||||
@param queue OpenCL command queue.
|
||||
"""
|
||||
self.context = context
|
||||
self.queue = queue
|
||||
self.program = clUtils.loadProgram(context, clUtils.path() + "/jacobi.cl")
|
||||
# Create OpenCL objects as null objects, that we will generate
|
||||
# at the first iteration
|
||||
self.A = None
|
||||
self.B = None
|
||||
self.X0 = None
|
||||
self.X = None
|
||||
self.x = None
|
||||
# Create dot operator
|
||||
self.dot = ReductionKernel(context, np.float32, neutral="0",
|
||||
reduce_expr="a+b", map_expr="x[i]*y[i]",
|
||||
arguments="__global float *x, __global float *y")
|
||||
|
||||
def solve(self, A, B, x0=None, tol=10e-6, iters=300, w=1.0):
|
||||
r""" Solve linear system of equations by a Jacobi
|
||||
iterative method.
|
||||
@param A Linear system matrix.
|
||||
@param B Linear system independent term.
|
||||
@param x0 Initial aproximation of the solution.
|
||||
@param tol Relative error tolerance: \n
|
||||
\$ \vert\vert B - A \, x \vert \vert_\infty /
|
||||
\vert\vert B \vert \vert_\infty \$
|
||||
@param iters Maximum number of iterations.
|
||||
@param w Relaxation factor
|
||||
"""
|
||||
# Create/set OpenCL buffers
|
||||
w = np.float32(w)
|
||||
self.setBuffers(A,B,x0)
|
||||
# Get dimensions for OpenCL execution
|
||||
n = np.uint32(len(B))
|
||||
gSize = (clUtils.globalSize(n),)
|
||||
# Get a norm to can compare later for valid result
|
||||
B_cl = cl_array.to_device(self.context,self.queue,B)
|
||||
bnorm2 = self.dot(B_cl,B_cl).get()
|
||||
w = w / bnorm2
|
||||
FreeCAD.Console.PrintMessage(bnorm2)
|
||||
FreeCAD.Console.PrintMessage("\n")
|
||||
rnorm2 = 0.
|
||||
# Iterate while the result converges or maximum number
|
||||
# of iterations is reached.
|
||||
for i in range(0,iters):
|
||||
kernelargs = (self.A,
|
||||
self.B,
|
||||
self.X0,
|
||||
self.X,
|
||||
n)
|
||||
# Test if the final result has been reached
|
||||
self.program.r(self.queue, gSize, None, *(kernelargs))
|
||||
cl.enqueue_read_buffer(self.queue, self.X, self.x).wait()
|
||||
x_cl = cl_array.to_device(self.context,self.queue,self.x)
|
||||
rnorm2 = self.dot(x_cl,x_cl).get()
|
||||
FreeCAD.Console.PrintMessage("\t")
|
||||
FreeCAD.Console.PrintMessage(rnorm2)
|
||||
FreeCAD.Console.PrintMessage("\n")
|
||||
if np.sqrt(rnorm2 / bnorm2) <= tol:
|
||||
break
|
||||
# Iterate
|
||||
kernelargs = (self.A,
|
||||
self.B,
|
||||
self.X0,
|
||||
self.X,
|
||||
w,
|
||||
n)
|
||||
self.program.jacobi(self.queue, gSize, None, *(kernelargs))
|
||||
kernelargs = (self.A,
|
||||
self.B,
|
||||
self.X,
|
||||
self.X0,
|
||||
w,
|
||||
n)
|
||||
self.program.jacobi(self.queue, gSize, None, *(kernelargs))
|
||||
# Return result computed
|
||||
cl.enqueue_read_buffer(self.queue, self.X0, self.x).wait()
|
||||
return (np.copy(self.x), np.sqrt(rnorm2 / bnorm2), i)
|
||||
|
||||
def setBuffers(self, A,B,x0):
|
||||
""" Create/set OpenCL required buffers.
|
||||
@param A Linear system matrix.
|
||||
@param B Independent linear term.
|
||||
@param x0 Initial solution estimator.
|
||||
"""
|
||||
# Get dimensions
|
||||
shape = np.shape(A)
|
||||
if len(shape) != 2:
|
||||
raise ValueError, 'Matrix A must be 2 dimensional array'
|
||||
if shape[0] != shape[1]:
|
||||
raise ValueError, 'Square linear system matrix expected'
|
||||
if len(B) != shape[0]:
|
||||
raise ValueError, 'Matrix and independet term dimensions does not match'
|
||||
n = len(B)
|
||||
# Set x0 if not provided
|
||||
if x0 != None:
|
||||
if len(x0) != n:
|
||||
raise ValueError, 'Initial solution estimator length does not match with linear system dimensions'
|
||||
if x0 == None:
|
||||
x0 = B
|
||||
# Create OpenCL objects if not already generated
|
||||
if not self.A:
|
||||
mf = cl.mem_flags
|
||||
self.A = cl.Buffer( self.context, mf.READ_ONLY, size = n*n * np.dtype('float32').itemsize )
|
||||
self.B = cl.Buffer( self.context, mf.READ_ONLY, size = n * np.dtype('float32').itemsize )
|
||||
self.X0 = cl.Buffer( self.context, mf.READ_WRITE, size = n * np.dtype('float32').itemsize )
|
||||
self.X = cl.Buffer( self.context, mf.READ_WRITE, size = n * np.dtype('float32').itemsize )
|
||||
self.x = np.zeros((n), dtype=np.float32)
|
||||
# Transfer data to buffers
|
||||
events = []
|
||||
events.append(cl.enqueue_write_buffer(self.queue, self.A, A.reshape((n*n)) ))
|
||||
events.append(cl.enqueue_write_buffer(self.queue, self.B, B))
|
||||
events.append(cl.enqueue_write_buffer(self.queue, self.X0, x0))
|
||||
for e in events:
|
||||
e.wait()
|
||||
|
||||
229
src/Mod/Ship/simRun/clSim/bem_lsqr_cl.py
Normal file
229
src/Mod/Ship/simRun/clSim/bem_lsqr_cl.py
Normal file
|
|
@ -0,0 +1,229 @@
|
|||
#***************************************************************************
|
||||
#* *
|
||||
#* Copyright (c) 2011, 2012 *
|
||||
#* Jose Luis Cercos Pita <jlcercos@gmail.com> *
|
||||
#* *
|
||||
#* This program is free software; you can redistribute it and/or modify *
|
||||
#* it under the terms of the GNU Lesser General Public License (LGPL) *
|
||||
#* as published by the Free Software Foundation; either version 2 of *
|
||||
#* the License, or (at your option) any later version. *
|
||||
#* for detail see the LICENCE text file. *
|
||||
#* *
|
||||
#* This program is distributed in the hope that it will be useful, *
|
||||
#* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||
#* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
|
||||
#* GNU Library General Public License for more details. *
|
||||
#* *
|
||||
#* You should have received a copy of the GNU Library General Public *
|
||||
#* License along with this program; if not, write to the Free Software *
|
||||
#* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 *
|
||||
#* USA *
|
||||
#* *
|
||||
#***************************************************************************
|
||||
|
||||
# numpy
|
||||
import numpy as np
|
||||
|
||||
# pyOpenCL
|
||||
import pyopencl as cl
|
||||
from pyopencl.reduction import ReductionKernel
|
||||
from pyopencl.elementwise import ElementwiseKernel
|
||||
import pyopencl.array as cl_array
|
||||
import clUtils
|
||||
|
||||
import FreeCAD
|
||||
grav=9.81
|
||||
|
||||
class lsqr:
|
||||
def __init__(self, context, queue):
|
||||
""" Constructor.
|
||||
@param context OpenCL context where apply.
|
||||
@param queue OpenCL command queue.
|
||||
"""
|
||||
self.context = context
|
||||
self.queue = queue
|
||||
self.program = clUtils.loadProgram(context, clUtils.path() + "/lsqr.cl")
|
||||
# Create OpenCL objects as null objects, that we will generate
|
||||
# at the first iteration
|
||||
self.A = None
|
||||
self.B = None
|
||||
self.X0 = None
|
||||
self.X = None
|
||||
self.R = None
|
||||
# Create dot operator
|
||||
self.dot = ReductionKernel(context, np.float32, neutral="0",
|
||||
reduce_expr="a+b", map_expr="x[i]*y[i]",
|
||||
arguments="__global float *x, __global float *y")
|
||||
self.dot_c_vec = ElementwiseKernel(context,
|
||||
"float c, float *v",
|
||||
"v[i] *= c")
|
||||
self.copy_vec = ElementwiseKernel(context,
|
||||
"float* out, float *in",
|
||||
"out[i] = in[i]")
|
||||
self.linear_comb = ElementwiseKernel(context,
|
||||
"float* z,"
|
||||
"float a, float *x, "
|
||||
"float b, float *y",
|
||||
"z[i] = a*x[i] + b*y[i]")
|
||||
self.prod = ElementwiseKernel(context,
|
||||
"float* z,"
|
||||
"float *x, float *y",
|
||||
"z[i] = x[i]*y[i]")
|
||||
|
||||
def solve(self, A, B, x0=None, tol=10e-6, iters=300):
|
||||
r""" Solve linear system of equations by a Jacobi
|
||||
iterative method.
|
||||
@param A Linear system matrix.
|
||||
@param B Linear system independent term.
|
||||
@param x0 Initial aproximation of the solution.
|
||||
@param tol Relative error tolerance: \n
|
||||
\$ \vert\vert B - A \, x \vert \vert_\infty /
|
||||
\vert\vert B \vert \vert_\infty \$
|
||||
@param iters Maximum number of iterations.
|
||||
"""
|
||||
# Create/set OpenCL buffers
|
||||
self.setBuffers(A,B,x0)
|
||||
# Get dimensions for OpenCL execution
|
||||
n = np.uint32(len(B))
|
||||
gSize = (clUtils.globalSize(n),)
|
||||
# Preconditionate matrix
|
||||
self.precondition(n)
|
||||
# Get a norm to can compare later for valid result
|
||||
bnorm = np.sqrt(self.dot(self.b,self.b).get())
|
||||
FreeCAD.Console.PrintMessage(bnorm)
|
||||
FreeCAD.Console.PrintMessage("\n")
|
||||
# Initialize the problem
|
||||
beta = bnorm
|
||||
self.dot_c_vec(1.0/beta, self.u)
|
||||
kernelargs = (self.A,self.u.data,self.v.data,n)
|
||||
self.program.dot_matT_vec(self.queue, gSize, None, *(kernelargs))
|
||||
alpha = np.sqrt(self.dot(self.v,self.v).get())
|
||||
self.dot_c_vec(1.0/alpha, self.v)
|
||||
self.copy_vec(self.w, self.v)
|
||||
rhobar = alpha
|
||||
phibar = beta
|
||||
# Iterate while the result converges or maximum number
|
||||
# of iterations is reached.
|
||||
for i in range(0,iters):
|
||||
# Compute residues
|
||||
kernelargs = (self.A,
|
||||
self.b.data,
|
||||
self.x.data,
|
||||
self.r.data,
|
||||
n)
|
||||
self.program.r(self.queue, gSize, None, *(kernelargs))
|
||||
rnorm = np.sqrt(self.dot(self.r,self.r).get())
|
||||
FreeCAD.Console.PrintMessage("\t")
|
||||
FreeCAD.Console.PrintMessage(rnorm)
|
||||
FreeCAD.Console.PrintMessage("\n")
|
||||
# Test if the final result has been reached
|
||||
if rnorm / bnorm <= tol:
|
||||
break
|
||||
# Compute next alpha, beta, u, v
|
||||
kernelargs = (self.A,self.u.data,self.v.data,self.u.data,alpha,n)
|
||||
self.program.u(self.queue, gSize, None, *(kernelargs))
|
||||
beta = np.sqrt(self.dot(self.u,self.u).get())
|
||||
FreeCAD.Console.PrintMessage("\t beta=")
|
||||
FreeCAD.Console.PrintMessage(beta)
|
||||
FreeCAD.Console.PrintMessage("\n")
|
||||
self.dot_c_vec(1.0/beta, self.u)
|
||||
kernelargs = (self.A,self.u.data,self.v.data,self.v.data,beta,n)
|
||||
self.program.v(self.queue, gSize, None, *(kernelargs))
|
||||
alpha = np.sqrt(self.dot(self.v,self.v).get())
|
||||
FreeCAD.Console.PrintMessage("\t alpha=")
|
||||
FreeCAD.Console.PrintMessage(alpha)
|
||||
FreeCAD.Console.PrintMessage("\n")
|
||||
self.dot_c_vec(1.0/alpha, self.v)
|
||||
# Apply the orthogonal transformation
|
||||
rho = np.sqrt(rhobar*rhobar + beta*beta)
|
||||
c = rhobar/rho
|
||||
s = beta*rho
|
||||
theta = s*alpha
|
||||
rhobar = -c*alpha
|
||||
phi = c*phibar
|
||||
phibar = s*phibar
|
||||
# Update x and w
|
||||
self.linear_comb(self.x, 1, self.x, phi/rho, self.w)
|
||||
self.linear_comb(self.w, 1, self.v, theta/rho, self.w)
|
||||
# Correct returned result due to the precoditioning
|
||||
self.prod(self.x, self.xf, self.x)
|
||||
# Return result computed
|
||||
x = np.zeros((n), dtype=np.float32)
|
||||
cl.enqueue_read_buffer(self.queue, self.x.data, x).wait()
|
||||
return (x, rnorm / bnorm, i)
|
||||
|
||||
def setBuffers(self, A,B,x0):
|
||||
""" Create/set OpenCL required buffers.
|
||||
@param A Linear system matrix.
|
||||
@param B Independent linear term.
|
||||
@param x0 Initial solution estimator.
|
||||
"""
|
||||
# Get dimensions
|
||||
shape = np.shape(A)
|
||||
if len(shape) != 2:
|
||||
raise ValueError, 'Matrix A must be 2 dimensional array'
|
||||
if shape[0] != shape[1]:
|
||||
raise ValueError, 'Square linear system matrix expected'
|
||||
if len(B) != shape[0]:
|
||||
raise ValueError, 'Matrix and independet term dimensions does not match'
|
||||
n = len(B)
|
||||
# Set x0 if not provided
|
||||
if x0 != None:
|
||||
if len(x0) != n:
|
||||
raise ValueError, 'Initial solution estimator length does not match with linear system dimensions'
|
||||
if x0 == None:
|
||||
x0 = B
|
||||
# Create OpenCL objects if not already generated
|
||||
if not self.A:
|
||||
mf = cl.mem_flags
|
||||
self.A = cl.Buffer( self.context, mf.READ_WRITE, size = n*n * np.dtype('float32').itemsize )
|
||||
self.b = cl_array.zeros(self.context,self.queue, (n), np.float32)
|
||||
self.x = cl_array.zeros(self.context,self.queue, (n), np.float32)
|
||||
self.xf = cl_array.zeros(self.context,self.queue, (n), np.float32)
|
||||
self.r = cl_array.zeros(self.context,self.queue, (n), np.float32)
|
||||
self.u = cl_array.zeros(self.context,self.queue, (n), np.float32)
|
||||
self.v = cl_array.zeros(self.context,self.queue, (n), np.float32)
|
||||
self.w = cl_array.zeros(self.context,self.queue, (n), np.float32)
|
||||
# Transfer data to buffers
|
||||
events = []
|
||||
events.append(cl.enqueue_write_buffer(self.queue, self.A, A.reshape((n*n)) ))
|
||||
self.b.set(B)
|
||||
self.x.set(x0)
|
||||
self.u.set(B)
|
||||
for e in events:
|
||||
e.wait()
|
||||
|
||||
def precondition(self, n):
|
||||
""" Preconditionate matrix, ensuring that all linear system
|
||||
matrix columns has an acceptable norm. Of course, final
|
||||
solution vector must be corrected conveniently.
|
||||
@param n Linear system dimension.
|
||||
"""
|
||||
gSize = (clUtils.globalSize(n),)
|
||||
xf = np.ones((n), dtype=np.float32)
|
||||
for i in range(0,n):
|
||||
col = np.uint32(i)
|
||||
# Compute column norm
|
||||
# We can use v as column vector because has not been used yet
|
||||
kernelargs = (self.A,
|
||||
self.v.data,
|
||||
col,
|
||||
n)
|
||||
self.program.column(self.queue, gSize, None, *(kernelargs))
|
||||
norm = np.sqrt(self.dot(self.v,self.v).get())
|
||||
FreeCAD.Console.PrintMessage("col ")
|
||||
FreeCAD.Console.PrintMessage(i)
|
||||
FreeCAD.Console.PrintMessage(", norm=")
|
||||
FreeCAD.Console.PrintMessage(norm)
|
||||
FreeCAD.Console.PrintMessage("\n")
|
||||
if norm < 1.0:
|
||||
continue
|
||||
fact = np.float32(1.0/norm)
|
||||
xf[i] = fact
|
||||
kernelargs = (self.A,
|
||||
fact,
|
||||
col,
|
||||
n)
|
||||
self.program.prod_c_column(self.queue, gSize, None, *(kernelargs))
|
||||
self.x.set(xf)
|
||||
|
||||
157
src/Mod/Ship/simRun/clSim/bem_minres_cl.py
Normal file
157
src/Mod/Ship/simRun/clSim/bem_minres_cl.py
Normal file
|
|
@ -0,0 +1,157 @@
|
|||
#***************************************************************************
|
||||
#* *
|
||||
#* Copyright (c) 2011, 2012 *
|
||||
#* Jose Luis Cercos Pita <jlcercos@gmail.com> *
|
||||
#* *
|
||||
#* This program is free software; you can redistribute it and/or modify *
|
||||
#* it under the terms of the GNU Lesser General Public License (LGPL) *
|
||||
#* as published by the Free Software Foundation; either version 2 of *
|
||||
#* the License, or (at your option) any later version. *
|
||||
#* for detail see the LICENCE text file. *
|
||||
#* *
|
||||
#* This program is distributed in the hope that it will be useful, *
|
||||
#* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||
#* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
|
||||
#* GNU Library General Public License for more details. *
|
||||
#* *
|
||||
#* You should have received a copy of the GNU Library General Public *
|
||||
#* License along with this program; if not, write to the Free Software *
|
||||
#* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 *
|
||||
#* USA *
|
||||
#* *
|
||||
#***************************************************************************
|
||||
|
||||
# numpy
|
||||
import numpy as np
|
||||
|
||||
# pyOpenCL
|
||||
import pyopencl as cl
|
||||
from pyopencl.reduction import ReductionKernel
|
||||
import pyopencl.array as cl_array
|
||||
import clUtils
|
||||
|
||||
import FreeCAD
|
||||
grav=9.81
|
||||
|
||||
class minres:
|
||||
def __init__(self, context, queue):
|
||||
""" Constructor.
|
||||
@param context OpenCL context where apply.
|
||||
@param queue OpenCL command queue.
|
||||
"""
|
||||
self.context = context
|
||||
self.queue = queue
|
||||
self.program = clUtils.loadProgram(context, clUtils.path() + "/minres.cl")
|
||||
# Create OpenCL objects as null objects, that we will generate
|
||||
# at the first iteration
|
||||
self.A = None
|
||||
self.B = None
|
||||
self.X0 = None
|
||||
self.X = None
|
||||
self.R = None
|
||||
# Create dot operator
|
||||
self.dot = ReductionKernel(context, np.float32, neutral="0",
|
||||
reduce_expr="a+b", map_expr="x[i]*y[i]",
|
||||
arguments="__global float *x, __global float *y")
|
||||
|
||||
def solve(self, A, B, x0=None, tol=10e-6, iters=300):
|
||||
r""" Solve linear system of equations by a Jacobi
|
||||
iterative method.
|
||||
@param A Linear system matrix.
|
||||
@param B Linear system independent term.
|
||||
@param x0 Initial aproximation of the solution.
|
||||
@param tol Relative error tolerance: \n
|
||||
\$ \vert\vert B - A \, x \vert \vert_\infty /
|
||||
\vert\vert B \vert \vert_\infty \$
|
||||
@param iters Maximum number of iterations.
|
||||
"""
|
||||
# Create/set OpenCL buffers
|
||||
self.setBuffers(A,B,x0)
|
||||
# Get dimensions for OpenCL execution
|
||||
n = np.uint32(len(B))
|
||||
gSize = (clUtils.globalSize(n),)
|
||||
# Get a norm to can compare later for valid result
|
||||
B_cl = cl_array.to_device(self.context,self.queue,B)
|
||||
bnorm2 = self.dot(B_cl,B_cl).get()
|
||||
FreeCAD.Console.PrintMessage(bnorm2)
|
||||
FreeCAD.Console.PrintMessage("\n")
|
||||
# Iterate while the result converges or maximum number
|
||||
# of iterations is reached.
|
||||
for i in range(0,iters):
|
||||
# Compute residues
|
||||
kernelargs = (self.A,
|
||||
self.B,
|
||||
self.X0,
|
||||
self.R.data,
|
||||
n)
|
||||
# Test if the final result has been reached
|
||||
self.program.r(self.queue, gSize, None, *(kernelargs))
|
||||
rnorm2 = self.dot(self.R,self.R).get()
|
||||
FreeCAD.Console.PrintMessage("\t")
|
||||
FreeCAD.Console.PrintMessage(rnorm2)
|
||||
FreeCAD.Console.PrintMessage("\n")
|
||||
if np.sqrt(rnorm2 / bnorm2) <= tol:
|
||||
break
|
||||
# Iterate
|
||||
kernelargs = (self.A,
|
||||
self.R.data,
|
||||
self.AR.data,
|
||||
n)
|
||||
self.program.dot_mat_vec(self.queue, gSize, None, *(kernelargs))
|
||||
AR_R = self.dot(self.AR,self.R).get()
|
||||
AR_AR = self.dot(self.AR,self.AR).get()
|
||||
kernelargs = (self.A,
|
||||
self.R.data,
|
||||
self.X,
|
||||
self.X0,
|
||||
AR_R,
|
||||
AR_AR,
|
||||
n)
|
||||
self.program.minres(self.queue, gSize, None, *(kernelargs))
|
||||
# Swap variables
|
||||
swap = self.X
|
||||
self.X = self.X0
|
||||
self.X0 = swap
|
||||
# Return result computed
|
||||
x = np.zeros((n), dtype=np.float32)
|
||||
cl.enqueue_read_buffer(self.queue, self.X0, x).wait()
|
||||
return (x, np.sqrt(rnorm2 / bnorm2), i)
|
||||
|
||||
def setBuffers(self, A,B,x0):
|
||||
""" Create/set OpenCL required buffers.
|
||||
@param A Linear system matrix.
|
||||
@param B Independent linear term.
|
||||
@param x0 Initial solution estimator.
|
||||
"""
|
||||
# Get dimensions
|
||||
shape = np.shape(A)
|
||||
if len(shape) != 2:
|
||||
raise ValueError, 'Matrix A must be 2 dimensional array'
|
||||
if shape[0] != shape[1]:
|
||||
raise ValueError, 'Square linear system matrix expected'
|
||||
if len(B) != shape[0]:
|
||||
raise ValueError, 'Matrix and independet term dimensions does not match'
|
||||
n = len(B)
|
||||
# Set x0 if not provided
|
||||
if x0 != None:
|
||||
if len(x0) != n:
|
||||
raise ValueError, 'Initial solution estimator length does not match with linear system dimensions'
|
||||
if x0 == None:
|
||||
x0 = B
|
||||
# Create OpenCL objects if not already generated
|
||||
if not self.A:
|
||||
mf = cl.mem_flags
|
||||
self.A = cl.Buffer( self.context, mf.READ_ONLY, size = n*n * np.dtype('float32').itemsize )
|
||||
self.B = cl.Buffer( self.context, mf.READ_ONLY, size = n * np.dtype('float32').itemsize )
|
||||
self.X0 = cl.Buffer( self.context, mf.READ_WRITE, size = n * np.dtype('float32').itemsize )
|
||||
self.X = cl.Buffer( self.context, mf.READ_WRITE, size = n * np.dtype('float32').itemsize )
|
||||
self.R = cl_array.zeros(self.context,self.queue, (n), np.float32)
|
||||
self.AR = cl_array.zeros(self.context,self.queue, (n), np.float32)
|
||||
# Transfer data to buffers
|
||||
events = []
|
||||
events.append(cl.enqueue_write_buffer(self.queue, self.A, A.reshape((n*n)) ))
|
||||
events.append(cl.enqueue_write_buffer(self.queue, self.B, B))
|
||||
events.append(cl.enqueue_write_buffer(self.queue, self.X0, x0))
|
||||
for e in events:
|
||||
e.wait()
|
||||
|
||||
58
src/Mod/Ship/simRun/clSim/clUtils.py
Normal file
58
src/Mod/Ship/simRun/clSim/clUtils.py
Normal file
|
|
@ -0,0 +1,58 @@
|
|||
#***************************************************************************
|
||||
#* *
|
||||
#* Copyright (c) 2011, 2012 *
|
||||
#* Jose Luis Cercos Pita <jlcercos@gmail.com> *
|
||||
#* *
|
||||
#* This program is free software; you can redistribute it and/or modify *
|
||||
#* it under the terms of the GNU Lesser General Public License (LGPL) *
|
||||
#* as published by the Free Software Foundation; either version 2 of *
|
||||
#* the License, or (at your option) any later version. *
|
||||
#* for detail see the LICENCE text file. *
|
||||
#* *
|
||||
#* This program is distributed in the hope that it will be useful, *
|
||||
#* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||
#* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
|
||||
#* GNU Library General Public License for more details. *
|
||||
#* *
|
||||
#* You should have received a copy of the GNU Library General Public *
|
||||
#* License along with this program; if not, write to the Free Software *
|
||||
#* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 *
|
||||
#* USA *
|
||||
#* *
|
||||
#***************************************************************************
|
||||
|
||||
# FreeCAD
|
||||
from shipUtils import Paths
|
||||
|
||||
# pyOpenCL
|
||||
import pyopencl as cl
|
||||
import numpy as np
|
||||
|
||||
# Standard
|
||||
import math
|
||||
|
||||
def loadProgram(context, file):
|
||||
""" Loads a file and comnpile it.
|
||||
@param context OpenCL context where apply.
|
||||
@param file File to load and compile.
|
||||
@return Ready to use OpenCL program.
|
||||
"""
|
||||
f = open(file, 'r')
|
||||
str = "".join(f.readlines())
|
||||
return cl.Program(context, str).build()
|
||||
|
||||
def path():
|
||||
""" Gets the OpenCL kernels path
|
||||
@return OpenCL kernels path
|
||||
"""
|
||||
path = Paths.modulePath() + "/resources/opencl"
|
||||
return path
|
||||
|
||||
def globalSize(n):
|
||||
""" Compute global size from amount of data.
|
||||
@param n Amount of data.
|
||||
@return global size.
|
||||
"""
|
||||
localSize = 256.0
|
||||
return int(math.ceil(n/localSize)*localSize)
|
||||
|
||||
258
src/Mod/Ship/simRun/clSim/evolution.py
Normal file
258
src/Mod/Ship/simRun/clSim/evolution.py
Normal file
|
|
@ -0,0 +1,258 @@
|
|||
#***************************************************************************
|
||||
#* *
|
||||
#* Copyright (c) 2011, 2012 *
|
||||
#* Jose Luis Cercos Pita <jlcercos@gmail.com> *
|
||||
#* *
|
||||
#* This program is free software; you can redistribute it and/or modify *
|
||||
#* it under the terms of the GNU Lesser General Public License (LGPL) *
|
||||
#* as published by the Free Software Foundation; either version 2 of *
|
||||
#* the License, or (at your option) any later version. *
|
||||
#* for detail see the LICENCE text file. *
|
||||
#* *
|
||||
#* This program is distributed in the hope that it will be useful, *
|
||||
#* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||
#* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
|
||||
#* GNU Library General Public License for more details. *
|
||||
#* *
|
||||
#* You should have received a copy of the GNU Library General Public *
|
||||
#* License along with this program; if not, write to the Free Software *
|
||||
#* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 *
|
||||
#* USA *
|
||||
#* *
|
||||
#***************************************************************************
|
||||
|
||||
# numpy
|
||||
import numpy as np
|
||||
import FreeCAD
|
||||
|
||||
grav=9.81
|
||||
|
||||
class simEvolution_cl:
|
||||
def __init__(self, context=None, queue=None):
|
||||
""" Constructor.
|
||||
@param context OpenCL context where apply. Only for compatibility,
|
||||
must be None.
|
||||
@param queue OpenCL command queue. Only for compatibility,
|
||||
must be None.
|
||||
"""
|
||||
self.context = context
|
||||
self.queue = queue
|
||||
|
||||
def execute(self, fs, bem, waves, t, dt):
|
||||
""" Compute the variables unknow for the next time step.
|
||||
@param fs Free surface instance.
|
||||
@param bem Boundary elements method instance.
|
||||
@param waves Waves instance.
|
||||
@param t Simulation time.
|
||||
@param dt Time step.
|
||||
"""
|
||||
self.BC(fs,bem,waves, t)
|
||||
self.Integrate(fs,bem,waves, t,dt)
|
||||
|
||||
def BC(self, fs, bem, waves, t):
|
||||
""" Apply the boundary conditions to compute time variation rate
|
||||
of the unknow variables.
|
||||
@param fs Free surface instance.
|
||||
@param bem Boundary elements method instance.
|
||||
@param waves Waves instance.
|
||||
@param t Simulation time.
|
||||
"""
|
||||
nx = fs['Nx']
|
||||
ny = fs['Ny']
|
||||
nFS = nx*ny
|
||||
for i in range(0,nx):
|
||||
for j in range(0,ny):
|
||||
gradp = np.copy(bem['gradp'][i*ny+j])
|
||||
z = fs['pos'][i,j,2]
|
||||
bem['dpdt'][i*ny+j] = - 0.5 * gradp**2.0 - 9.81*z
|
||||
fs['vel'][i,j,2] = gradp
|
||||
# Since the inverse method returns significant errors near
|
||||
# to the free surface borders, we will modify 3 area
|
||||
# elements of the border such that the last one will be
|
||||
# exactly the analytic solution. Also we will use it as
|
||||
# numerical beach in order to disipate waves generated
|
||||
# inside the domain (that will be refelceted otherwise)
|
||||
# 1.- Corners
|
||||
for i in range(0,4)+range(nx-4,nx):
|
||||
if i in range(0,4):
|
||||
fx = 1. - i/4.
|
||||
else:
|
||||
fx = (i - nx + 5) / 4.
|
||||
for j in range(0,4)+range(ny-4,ny):
|
||||
if j in range(0,4):
|
||||
fy = 1. - j/4.
|
||||
else:
|
||||
fy = (j - ny + 5) / 4.
|
||||
factor = max(fx,fy)
|
||||
pos = fs['pos'][i,j]
|
||||
dpdt = 0.
|
||||
vel = 0.
|
||||
for w in waves['data']:
|
||||
A = w[0]
|
||||
T = w[1]
|
||||
phase = w[2]
|
||||
heading = np.pi*w[3]/180.0
|
||||
wl = 0.5 * grav / np.pi * T*T
|
||||
k = 2.0*np.pi/wl
|
||||
frec = 2.0*np.pi/T
|
||||
l = pos[0]*np.cos(heading) + pos[1]*np.sin(heading)
|
||||
amp = - A*9.81*np.sin(k*l - frec*t + phase)*np.exp(k*pos[2])
|
||||
dpdt = dpdt + amp
|
||||
amp = - A*frec*np.cos(k*l - frec*t + phase)
|
||||
vel = vel + amp
|
||||
bem['dpdt'][i*ny+j] = factor*dpdt + (1.-factor)*bem['dpdt'][i*ny+j]
|
||||
fs['vel'][i,j,2] = factor*vel + (1.-factor)*fs['vel'][i,j,2]
|
||||
# 2.- rows
|
||||
for i in range(0,4)+range(nx-4,nx):
|
||||
if i in range(0,4):
|
||||
factor = 1. - i/4.
|
||||
else:
|
||||
factor = (i - nx + 5) / 4.
|
||||
for j in range(4, ny-4):
|
||||
pos = fs['pos'][i,j]
|
||||
dpdt = 0.
|
||||
vel = 0.
|
||||
for w in waves['data']:
|
||||
A = w[0]
|
||||
T = w[1]
|
||||
phase = w[2]
|
||||
heading = np.pi*w[3]/180.0
|
||||
wl = 0.5 * grav / np.pi * T*T
|
||||
k = 2.0*np.pi/wl
|
||||
frec = 2.0*np.pi/T
|
||||
l = pos[0]*np.cos(heading) + pos[1]*np.sin(heading)
|
||||
amp = - A*9.81*np.sin(k*l - frec*t + phase)*np.exp(k*pos[2])
|
||||
dpdt = dpdt + amp
|
||||
amp = - A*frec*np.cos(k*l - frec*t + phase)
|
||||
vel = vel + amp
|
||||
bem['dpdt'][i*ny+j] = factor*dpdt + (1.-factor)*bem['dpdt'][i*ny+j]
|
||||
fs['vel'][i,j,2] = factor*vel + (1.-factor)*fs['vel'][i,j,2]
|
||||
# 3.- columns
|
||||
for j in range(0,4)+range(ny-4,ny):
|
||||
if j in range(0,4):
|
||||
factor = 1. - j/4.
|
||||
else:
|
||||
factor = (j - ny + 5) / 4.
|
||||
for i in range(4, nx-4):
|
||||
pos = fs['pos'][i,j]
|
||||
dpdt = 0.
|
||||
vel = 0.
|
||||
for w in waves['data']:
|
||||
A = w[0]
|
||||
T = w[1]
|
||||
phase = w[2]
|
||||
heading = np.pi*w[3]/180.0
|
||||
wl = 0.5 * grav / np.pi * T*T
|
||||
k = 2.0*np.pi/wl
|
||||
frec = 2.0*np.pi/T
|
||||
l = pos[0]*np.cos(heading) + pos[1]*np.sin(heading)
|
||||
amp = - A*9.81*np.sin(k*l - frec*t + phase)*np.exp(k*pos[2])
|
||||
dpdt = dpdt + amp
|
||||
amp = - A*frec*np.cos(k*l - frec*t + phase)
|
||||
vel = vel + amp
|
||||
bem['dpdt'][i*ny+j] = factor*dpdt + (1.-factor)*bem['dpdt'][i*ny+j]
|
||||
fs['vel'][i,j,2] = factor*vel + (1.-factor)*fs['vel'][i,j,2]
|
||||
|
||||
def Integrate(self, fs, bem, waves, t, dt):
|
||||
""" Perform time integration of the unknow variables.
|
||||
@param fs Free surface instance.
|
||||
@param bem Boundary elements method instance.
|
||||
@param waves Waves instance.
|
||||
@param t Simulation time.
|
||||
@param dt Time step.
|
||||
"""
|
||||
nx = fs['Nx']
|
||||
ny = fs['Ny']
|
||||
nFS = nx*ny
|
||||
for i in range(0,nx):
|
||||
for j in range(0,ny):
|
||||
bem['p'][i*ny+j] = bem['p'][i*ny+j] + dt * bem['dpdt'][i*ny+j]
|
||||
fs['pos'][i,j,2] = fs['pos'][i,j,2] + dt * fs['vel'][i,j,2]
|
||||
# Since the inverse method returns significant errors near
|
||||
# to the free surface borders, we will modify 3 area
|
||||
# elements of the border such that the last one will be
|
||||
# exactly the analytic solution. Also we will use it as
|
||||
# numerical beach in order to disipate waves generated
|
||||
# inside the domain (that will be refelceted otherwise)
|
||||
# 1.- Corners
|
||||
for i in range(0,4)+range(nx-4,nx):
|
||||
if i in range(0,4):
|
||||
fx = 1. - i/4.
|
||||
else:
|
||||
fx = (i - nx + 5) / 4.
|
||||
for j in range(0,4)+range(ny-4,ny):
|
||||
if j in range(0,4):
|
||||
fy = 1. - j/4.
|
||||
else:
|
||||
fy = (j - ny + 5) / 4.
|
||||
factor = max(fx,fy)
|
||||
pos = fs['pos'][i,j]
|
||||
phi = 0.
|
||||
z = 0.
|
||||
for w in waves['data']:
|
||||
A = w[0]
|
||||
T = w[1]
|
||||
phase = w[2]
|
||||
heading = np.pi*w[3]/180.0
|
||||
wl = 0.5 * grav / np.pi * T*T
|
||||
k = 2.0*np.pi/wl
|
||||
frec = 2.0*np.pi/T
|
||||
l = pos[0]*np.cos(heading) + pos[1]*np.sin(heading)
|
||||
amp = - A*frec/k*np.cos(k*l - frec*(t+dt) + phase)*np.exp(k*pos[2])
|
||||
phi = phi + amp
|
||||
amp = A*np.sin(k*l - frec*(t+dt) + phase)
|
||||
z = z + amp
|
||||
bem['p'][i*ny+j] = factor*phi + (1.-factor)*bem['p'][i*ny+j]
|
||||
fs['pos'][i,j,2] = factor*z + (1.-factor)*fs['pos'][i,j,2]
|
||||
# 2.- rows
|
||||
for i in range(0,4)+range(nx-4,nx):
|
||||
if i in range(0,4):
|
||||
factor = 1. - i/4.
|
||||
else:
|
||||
factor = (i - nx + 5) / 4.
|
||||
for j in range(4, ny-4):
|
||||
pos = fs['pos'][i,j]
|
||||
phi = 0.
|
||||
z = 0.
|
||||
for w in waves['data']:
|
||||
A = w[0]
|
||||
T = w[1]
|
||||
phase = w[2]
|
||||
heading = np.pi*w[3]/180.0
|
||||
wl = 0.5 * grav / np.pi * T*T
|
||||
k = 2.0*np.pi/wl
|
||||
frec = 2.0*np.pi/T
|
||||
l = pos[0]*np.cos(heading) + pos[1]*np.sin(heading)
|
||||
amp = - A*frec/k*np.cos(k*l - frec*(t+dt) + phase)*np.exp(k*pos[2])
|
||||
phi = phi + amp
|
||||
amp = A*np.sin(k*l - frec*(t+dt) + phase)
|
||||
z = z + amp
|
||||
bem['p'][i*ny+j] = factor*phi + (1.-factor)*bem['p'][i*ny+j]
|
||||
fs['pos'][i,j,2] = factor*z + (1.-factor)*fs['pos'][i,j,2]
|
||||
# 3.- columns
|
||||
for j in range(0,4)+range(ny-4,ny):
|
||||
if j in range(0,4):
|
||||
factor = 1. - j/4.
|
||||
else:
|
||||
factor = (j - ny + 5) / 4.
|
||||
for i in range(4, nx-4):
|
||||
pos = fs['pos'][i,j]
|
||||
phi = 0.
|
||||
z = 0.
|
||||
for w in waves['data']:
|
||||
A = w[0]
|
||||
T = w[1]
|
||||
phase = w[2]
|
||||
heading = np.pi*w[3]/180.0
|
||||
wl = 0.5 * grav / np.pi * T*T
|
||||
k = 2.0*np.pi/wl
|
||||
frec = 2.0*np.pi/T
|
||||
l = pos[0]*np.cos(heading) + pos[1]*np.sin(heading)
|
||||
amp = - A*frec/k*np.cos(k*l - frec*(t+dt) + phase)*np.exp(k*pos[2])
|
||||
phi = phi + amp
|
||||
amp = A*np.sin(k*l - frec*(t+dt) + phase)
|
||||
z = z + amp
|
||||
bem['p'][i*ny+j] = factor*phi + (1.-factor)*bem['p'][i*ny+j]
|
||||
fs['pos'][i,j,2] = factor*z + (1.-factor)*fs['pos'][i,j,2]
|
||||
|
||||
|
||||
|
|
@ -1,113 +1,229 @@
|
|||
#***************************************************************************
|
||||
#* *
|
||||
#* Copyright (c) 2011, 2012 *
|
||||
#* Jose Luis Cercos Pita <jlcercos@gmail.com> *
|
||||
#* *
|
||||
#* *
|
||||
#* Copyright (c) 2011, 2012 *
|
||||
#* Jose Luis Cercos Pita <jlcercos@gmail.com> *
|
||||
#* *
|
||||
#* This program is free software; you can redistribute it and/or modify *
|
||||
#* it under the terms of the GNU Lesser General Public License (LGPL) *
|
||||
#* as published by the Free Software Foundation; either version 2 of *
|
||||
#* the License, or (at your option) any later version. *
|
||||
#* for detail see the LICENCE text file. *
|
||||
#* *
|
||||
#* This program is distributed in the hope that it will be useful, *
|
||||
#* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||
#* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
|
||||
#* GNU Library General Public License for more details. *
|
||||
#* *
|
||||
#* You should have received a copy of the GNU Library General Public *
|
||||
#* it under the terms of the GNU Lesser General Public License (LGPL) *
|
||||
#* as published by the Free Software Foundation; either version 2 of *
|
||||
#* the License, or (at your option) any later version. *
|
||||
#* for detail see the LICENCE text file. *
|
||||
#* *
|
||||
#* This program is distributed in the hope that it will be useful, *
|
||||
#* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||
#* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
|
||||
#* GNU Library General Public License for more details. *
|
||||
#* *
|
||||
#* You should have received a copy of the GNU Library General Public *
|
||||
#* License along with this program; if not, write to the Free Software *
|
||||
#* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 *
|
||||
#* USA *
|
||||
#* *
|
||||
#* USA *
|
||||
#* *
|
||||
#***************************************************************************
|
||||
|
||||
# Simulation stuff
|
||||
from Utils import *
|
||||
|
||||
# pyOpenCL
|
||||
import pyopencl as cl
|
||||
# numpy
|
||||
import numpy as np
|
||||
import FreeCAD
|
||||
|
||||
class perform:
|
||||
def __init__(self, FSmesh, waves, context, queue):
|
||||
""" Constructor, includes program loading.
|
||||
@param FSmesh Initial free surface mesh.
|
||||
@param waves Considered simulation waves (A,T,phi,heading).
|
||||
@param context OpenCL context where apply.
|
||||
@param queue OpenCL command queue.
|
||||
"""
|
||||
self.context = context
|
||||
self.queue = queue
|
||||
self.program = loadProgram(context, clPath() + "/simInit.cl")
|
||||
self.loadData(FSmesh, waves)
|
||||
self.execute()
|
||||
grav=9.81
|
||||
|
||||
class simInitialization_cl:
|
||||
def __init__(self, FSMesh, FSData, waves, Sea, context=None, queue=None):
|
||||
""" Constructor.
|
||||
@param FSMesh Initial free surface mesh.
|
||||
@param FSData Dimensions data of the free surface mesh (L,B,Nx,Ny)
|
||||
@param waves Considered simulation waves (A,T,phi,heading).
|
||||
@param Sea Tuple with the number of free surfaces that must be repeated in each direction.
|
||||
@param context OpenCL context where apply. Only for compatibility,
|
||||
must be None.
|
||||
@param queue OpenCL command queue. Only for compatibility,
|
||||
must be None.
|
||||
"""
|
||||
self.context = context
|
||||
self.queue = queue
|
||||
self.loadData(FSMesh, FSData, waves, Sea)
|
||||
self.execute()
|
||||
# Compute time step
|
||||
self.dt = 0.1
|
||||
for w in self.waves['data']:
|
||||
if(self.dt > w[1]/200.0):
|
||||
self.dt = w[1]/200.0
|
||||
|
||||
def loadData(self, FSMesh, FSData, waves, Sea):
|
||||
""" Convert data to numpy format.
|
||||
@param FSMesh Initial free surface mesh.
|
||||
@param FSData Dimensions data of the free surface mesh (L,B,Nx,Ny)
|
||||
@param waves Considered simulation waves (A,T,phi,heading).
|
||||
@param Sea Tuple with the number of free surfaces that must be repeated in each direction.
|
||||
"""
|
||||
# Data will classified in four groups:
|
||||
# Free surface:
|
||||
# Is a key part of the simulation, so is
|
||||
# separated from the rest of water involved
|
||||
# elements.
|
||||
# Sea:
|
||||
# BEM method requires to artificially extend
|
||||
# the free surface in order to send the bounds
|
||||
# Inlet, Outlet, Left and Side to the infinite.
|
||||
# Here is specified how many time must be
|
||||
# repeated the free surface in order to get
|
||||
# virtually infinite far bounds.
|
||||
# Body:
|
||||
# Is the main objective of the simulation.
|
||||
# Waves:
|
||||
# Data that is append as boundary condition.
|
||||
# BEM:
|
||||
# Used to solve the BEM problem and evolution.
|
||||
|
||||
# --------------------------------------------
|
||||
# Free surface data
|
||||
# N, Nx, Ny = Number of points in each
|
||||
# direction
|
||||
# pos = Positions
|
||||
# vel = Velocities
|
||||
# n = Normals
|
||||
# area = Areas
|
||||
# --------------------------------------------
|
||||
nx = len(FSMesh)
|
||||
ny = len(FSMesh[0])
|
||||
L = FSData[0]
|
||||
B = FSData[1]
|
||||
dx = L/nx
|
||||
dy = B/ny
|
||||
p = np.zeros((nx,ny, 4), dtype=np.float32)
|
||||
V = np.zeros((nx,ny, 4), dtype=np.float32)
|
||||
n = np.zeros((nx,ny, 4), dtype=np.float32)
|
||||
a = np.ndarray((nx,ny), dtype=np.float32)
|
||||
for i in range(0, nx):
|
||||
for j in range(0, ny):
|
||||
pos = FSMesh[i][j].pos
|
||||
normal = FSMesh[i][j].normal
|
||||
area = FSMesh[i][j].area
|
||||
p[i,j,0] = pos.x
|
||||
p[i,j,1] = pos.y
|
||||
p[i,j,2] = pos.z
|
||||
p[i,j,3] = 1.0
|
||||
n[i,j,0] = normal.x
|
||||
n[i,j,1] = normal.y
|
||||
n[i,j,2] = normal.z
|
||||
a[i,j] = area
|
||||
self.fs = {'N':nx*ny, 'Nx':nx, 'Ny':ny, \
|
||||
'L':L, 'B':B, 'dx':dx, 'dy':dy, \
|
||||
'pos':p, 'vel':V, 'normal':n, 'area':a}
|
||||
# --------------------------------------------
|
||||
# Sea data
|
||||
# N, Nx, Ny = Number of free surfaces
|
||||
# repetitions in each direction
|
||||
# --------------------------------------------
|
||||
self.sea = {'N':Sea[0]*Sea[1], 'Nx':Sea[0], 'Ny':Sea[1]}
|
||||
# --------------------------------------------
|
||||
# Body data
|
||||
# N, Nx, Ny = Number of points in each
|
||||
# direction
|
||||
# pos = Positions
|
||||
# vel = Velocities
|
||||
# n = Normals
|
||||
# area = Areas
|
||||
# --------------------------------------------
|
||||
self.b = {'N':0, 'pos':None, 'vel':None, 'normal':None, 'area':None}
|
||||
# --------------------------------------------
|
||||
# Waves data
|
||||
# N = Number of waves
|
||||
# data = Waves data
|
||||
# --------------------------------------------
|
||||
nW = len(waves)
|
||||
w = np.ndarray((nW, 4), dtype=np.float32)
|
||||
for i in range(0,nW):
|
||||
w[i,0] = waves[i][0]
|
||||
w[i,1] = waves[i][1]
|
||||
w[i,2] = waves[i][2]
|
||||
w[i,3] = waves[i][3]
|
||||
self.waves = {'N':nW, 'data':w}
|
||||
# --------------------------------------------
|
||||
# BEM data
|
||||
# N = nFS + nB
|
||||
# A,B = Linear system matrix and vectors
|
||||
# p = Velocity potentials (phi).
|
||||
# gradp = Velocity potentials gradient
|
||||
# (grad(phi)) projected over the
|
||||
# normal
|
||||
# dpdt = Velocity potentials time
|
||||
# variation rate
|
||||
# --------------------------------------------
|
||||
nFS = self.fs['N']
|
||||
nB = self.b['N']
|
||||
N = nFS + nB
|
||||
A = np.zeros((N, N), dtype=np.float32)
|
||||
B = np.zeros((N), dtype=np.float32)
|
||||
p = np.zeros((N), dtype=np.float32)
|
||||
gp = np.zeros((N), dtype=np.float32)
|
||||
dpdt = np.zeros((N), dtype=np.float32)
|
||||
self.bem = {'N':N, 'A':A, 'B':B, \
|
||||
'p':p, 'gradp':gp, 'dpdt':dpdt }
|
||||
|
||||
def execute(self):
|
||||
""" Compute initial conditions. """
|
||||
# --------------------------------------------
|
||||
# Free surface initial condition.
|
||||
# Since RK4 scheme starts on the end of
|
||||
# previous step, we only write on last
|
||||
# stage value (p4 and dp4)
|
||||
# --------------------------------------------
|
||||
nx = self.fs['Nx']
|
||||
ny = self.fs['Ny']
|
||||
for i in range(0,nx):
|
||||
for j in range(0,ny):
|
||||
# Since initial values of the potencial, and this acceleration,
|
||||
# depends on z, we need to compute first the positions.
|
||||
self.fs['pos'][i,j][2] = 0.
|
||||
self.bem['p'][i*ny+j] = 0.
|
||||
self.bem['gradp'][i*ny+j] = 0.
|
||||
for w in self.waves['data']:
|
||||
A = w[0]
|
||||
T = w[1]
|
||||
phase = w[2]
|
||||
heading = np.pi*w[3]/180.0
|
||||
wl = 0.5 * grav / np.pi * T*T
|
||||
k = 2.0*np.pi/wl
|
||||
frec = 2.0*np.pi/T
|
||||
pos = self.fs['pos'][i,j]
|
||||
l = pos[0]*np.cos(heading) + pos[1]*np.sin(heading)
|
||||
amp = A*np.sin(k*l + phase)
|
||||
self.fs['pos'][i,j][2] = self.fs['pos'][i,j][2] + amp
|
||||
amp = - A*frec*np.cos(k*l + phase)
|
||||
self.fs['vel'][i,j][2] = self.fs['vel'][i,j][2] + amp
|
||||
# And now we can compute potentials.
|
||||
for w in self.waves['data']:
|
||||
A = w[0]
|
||||
T = w[1]
|
||||
phase = w[2]
|
||||
heading = np.pi*w[3]/180.0
|
||||
wl = 0.5 * grav / np.pi * T*T
|
||||
k = 2.0*np.pi/wl
|
||||
frec = 2.0*np.pi/T
|
||||
pos = self.fs['pos'][i,j]
|
||||
l = pos[0]*np.cos(heading) + pos[1]*np.sin(heading)
|
||||
amp = - A*frec/k*np.cos(k*l + phase)*np.exp(k*pos[2])
|
||||
self.bem['p'][i*ny+j] = self.bem['p'][i*ny+j] + amp
|
||||
amp = - A*frec*np.cos(k*l + phase)*np.exp(k*pos[2])
|
||||
self.bem['gradp'][i*ny+j] = self.bem['gradp'][i*ny+j] + amp
|
||||
|
||||
# --------------------------------------------------------
|
||||
# Debugging
|
||||
# --------------------------------------------------------
|
||||
"""
|
||||
self.fs['pos'][i,j][2] = 0.
|
||||
self.bem['p'][i*ny+j] = 0.
|
||||
self.bem['gradp'][i*ny+j] = 0.
|
||||
# We can do phi = Green's function
|
||||
dx = self.fs['pos'][i,j][0]
|
||||
dy = self.fs['pos'][i,j][1]
|
||||
dz = 15.0 # An arbitrary value > 0
|
||||
self.bem['p'][i*ny+j] = 1. / (4. * np.pi * np.sqrt(dx*dx + dy*dy + dz*dz))
|
||||
self.bem['gradp'][i*ny+j] = - dz / (4. * np.pi * (dx*dx + dy*dy + dz*dz)**(1.5))
|
||||
"""
|
||||
# --------------------------------------------------------
|
||||
# Debugging
|
||||
# --------------------------------------------------------
|
||||
|
||||
def loadData(self, FSmesh, waves):
|
||||
""" Convert data to numpy format, and create OpenCL
|
||||
buffers.
|
||||
@param FSmesh Initial free surface mesh.
|
||||
@param waves Considered simulation waves (A,T,phi,heading).
|
||||
"""
|
||||
mf = cl.mem_flags
|
||||
nx = len(FSmesh)
|
||||
ny = len(FSmesh[0])
|
||||
nW = len(waves)
|
||||
# Mesh data
|
||||
p = np.ndarray((nx*ny, 4), dtype=np.float32)
|
||||
n = np.ndarray((nx*ny, 4), dtype=np.float32)
|
||||
a = np.ndarray((nx*ny, 1), dtype=np.float32)
|
||||
for i in range(0, nx):
|
||||
for j in range(0, ny):
|
||||
id = i*ny + j
|
||||
pos = FSmesh[i][j].pos
|
||||
normal = FSmesh[i][j].normal
|
||||
area = FSmesh[i][j].area
|
||||
p[id,0] = pos.x
|
||||
p[id,1] = pos.y
|
||||
p[id,2] = pos.z
|
||||
p[id,3] = 1.
|
||||
n[id,0] = normal.x
|
||||
n[id,1] = normal.y
|
||||
n[id,2] = normal.z
|
||||
n[id,3] = 0.
|
||||
a[id,0] = area
|
||||
p_cl = cl.Buffer(self.context, mf.READ_WRITE | mf.COPY_HOST_PTR, hostbuf=p)
|
||||
n_cl = cl.Buffer(self.context, mf.READ_WRITE | mf.COPY_HOST_PTR, hostbuf=n)
|
||||
a_cl = cl.Buffer(self.context, mf.READ_WRITE | mf.COPY_HOST_PTR, hostbuf=a)
|
||||
v_cl = cl.Buffer(self.context, mf.READ_WRITE, size = nx*ny*4 * np.dtype('float32').itemsize)
|
||||
f_cl = cl.Buffer(self.context, mf.READ_WRITE, size = nx*ny*4 * np.dtype('float32').itemsize)
|
||||
phi = cl.Buffer(self.context, mf.READ_WRITE, size = nx*ny * np.dtype('float32').itemsize)
|
||||
Phi = cl.Buffer(self.context, mf.READ_WRITE, size = nx*ny * np.dtype('float32').itemsize)
|
||||
self.fs = {'Nx':nx, 'Ny':ny, 'pos':p_cl, 'vel':v_cl, 'acc':f_cl, \
|
||||
'normal':n_cl, 'area':a_cl, 'velPot':phi, 'accPot':Phi}
|
||||
# Waves data
|
||||
w = np.ndarray((nW, 4), dtype=np.float32)
|
||||
for i in range(0,nW):
|
||||
w[i,0] = waves[i][0]
|
||||
w[i,1] = waves[i][1]
|
||||
w[i,2] = waves[i][2]
|
||||
w[i,3] = waves[i][3]
|
||||
w_cl = cl.Buffer(self.context, mf.READ_WRITE | mf.COPY_HOST_PTR, hostbuf=w)
|
||||
self.waves = {'N':nW, 'data':w_cl}
|
||||
# Ensure that all data has been written
|
||||
self.queue.finish()
|
||||
|
||||
def execute(self):
|
||||
""" Compute initial conditions. """
|
||||
# Global size computation
|
||||
N = np.ndarray((2, 1), dtype=np.uint32)
|
||||
N[0] = self.fs['Nx']
|
||||
N[1] = self.fs['Ny']
|
||||
n = np.uint32(self.waves['N'])
|
||||
gSize = (globalSize(N[0]),globalSize(N[1]),)
|
||||
# Kernel arguments
|
||||
kernelargs = (self.fs['pos'],
|
||||
self.fs['vel'],
|
||||
self.fs['acc'],
|
||||
self.waves['data'],
|
||||
self.fs['velPot'],
|
||||
self.fs['accPot'],
|
||||
N, n)
|
||||
# Kernel launch
|
||||
self.program.FS(self.queue, gSize, None, *(kernelargs))
|
||||
self.queue.finish()
|
||||
|
|
|
|||
184
src/Mod/Ship/simRun/clSim/matrixGen.py
Normal file
184
src/Mod/Ship/simRun/clSim/matrixGen.py
Normal file
|
|
@ -0,0 +1,184 @@
|
|||
#***************************************************************************
|
||||
#* *
|
||||
#* Copyright (c) 2011, 2012 *
|
||||
#* Jose Luis Cercos Pita <jlcercos@gmail.com> *
|
||||
#* *
|
||||
#* This program is free software; you can redistribute it and/or modify *
|
||||
#* it under the terms of the GNU Lesser General Public License (LGPL) *
|
||||
#* as published by the Free Software Foundation; either version 2 of *
|
||||
#* the License, or (at your option) any later version. *
|
||||
#* for detail see the LICENCE text file. *
|
||||
#* *
|
||||
#* This program is distributed in the hope that it will be useful, *
|
||||
#* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||
#* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
|
||||
#* GNU Library General Public License for more details. *
|
||||
#* *
|
||||
#* You should have received a copy of the GNU Library General Public *
|
||||
#* License along with this program; if not, write to the Free Software *
|
||||
#* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 *
|
||||
#* USA *
|
||||
#* *
|
||||
#***************************************************************************
|
||||
|
||||
# numpy
|
||||
import numpy as np
|
||||
|
||||
# pyOpenCL
|
||||
import pyopencl as cl
|
||||
import clUtils
|
||||
|
||||
import FreeCAD
|
||||
grav=9.81
|
||||
|
||||
class simMatrixGen_cl:
|
||||
def __init__(self, context=None, queue=None):
|
||||
""" Constructor.
|
||||
@param context OpenCL context where apply.
|
||||
@param queue OpenCL command queue.
|
||||
"""
|
||||
self.context = context
|
||||
self.queue = queue
|
||||
self.program = clUtils.loadProgram(context, clUtils.path() + "/matrixGen.cl")
|
||||
# Create OpenCL objects as null objects, that we will generate
|
||||
# at the first iteration
|
||||
self.A = None
|
||||
self.B = None
|
||||
self.dB = None
|
||||
self.pos = None
|
||||
self.area = None
|
||||
self.normal = None
|
||||
self.p = None
|
||||
self.gradp = None
|
||||
|
||||
def execute(self, fs, waves, sea, bem, body, t):
|
||||
""" Compute system matrix.
|
||||
@param fs Free surface instance.
|
||||
@param waves Waves instance.
|
||||
@param sea Sea boundary instance.
|
||||
@param bem Boundary Element Method instance.
|
||||
@param body Body instance.
|
||||
@param t Simulation time.
|
||||
"""
|
||||
# Create/set OpenCL buffers
|
||||
self.setBuffers(fs,waves,sea,bem,body)
|
||||
# Convert constant parameters
|
||||
L = np.float32(fs['L'])
|
||||
B = np.float32(fs['B'])
|
||||
dx = np.float32(fs['dx'])
|
||||
dy = np.float32(fs['dy'])
|
||||
T = np.float32(t)
|
||||
# Get dimensions for OpenCL execution
|
||||
nx = np.uint32(fs['Nx'])
|
||||
ny = np.uint32(fs['Ny'])
|
||||
nFS = np.uint32(fs['N'])
|
||||
nB = np.uint32(body['N'])
|
||||
n = np.uint32(nFS + nB)
|
||||
nSeax = np.int32(sea['Nx'])
|
||||
nSeay = np.int32(sea['Ny'])
|
||||
nW = np.uint32(waves['N'])
|
||||
# Call OpenCL to work
|
||||
gSize = (clUtils.globalSize(n),)
|
||||
kernelargs = (self.A,
|
||||
self.B,
|
||||
self.pos,
|
||||
self.area,
|
||||
self.normal,
|
||||
self.bem_p,
|
||||
self.bem_dp,
|
||||
self.waves,
|
||||
L,
|
||||
B,
|
||||
dx,
|
||||
dy,
|
||||
T,
|
||||
nx,
|
||||
ny,
|
||||
nFS,
|
||||
nB,
|
||||
n,
|
||||
nSeax,
|
||||
nSeay,
|
||||
nW)
|
||||
self.program.matrixGen(self.queue, gSize, None, *(kernelargs))
|
||||
self.queue.finish()
|
||||
# Read output data
|
||||
events = []
|
||||
events.append(cl.enqueue_read_buffer(self.queue, self.A, bem['A'].reshape((n*n))))
|
||||
events.append(cl.enqueue_read_buffer(self.queue, self.B, bem['B']))
|
||||
# events.append(cl.enqueue_read_buffer(self.queue, self.dB, bem['dB']))
|
||||
for e in events:
|
||||
e.wait()
|
||||
|
||||
|
||||
# --------------------------------------------------------
|
||||
# Debugging
|
||||
# --------------------------------------------------------
|
||||
"""
|
||||
for i in range(0,fs['Nx']):
|
||||
for j in range(0,fs['Ny']):
|
||||
x = fs['pos'][i,j,0]
|
||||
y = fs['pos'][i,j,1]
|
||||
FreeCAD.Console.PrintMessage("pos = {0},{1}\n".format(x,y))
|
||||
A = np.dot(bem['A'][i*fs['Ny'] + j,:], bem['gradp'][:])
|
||||
B = bem['B'][i*fs['Ny'] + j]
|
||||
phi = 2.0 * (B - A)
|
||||
bem['p'][i*fs['Ny'] + j] = phi
|
||||
"""
|
||||
|
||||
# --------------------------------------------------------
|
||||
# Debugging
|
||||
# --------------------------------------------------------
|
||||
return
|
||||
|
||||
def setBuffers(self, fs, waves, sea, bem, body):
|
||||
""" Create/set OpenCL required buffers.
|
||||
@param fs Free surface instance.
|
||||
@param waves Waves instance.
|
||||
@param sea Sea boundary instance.
|
||||
@param bem Boundary Element Method instance.
|
||||
@param body Body instance.
|
||||
"""
|
||||
# Get dimensions
|
||||
nFS = fs['N']
|
||||
nB = body['N']
|
||||
n = nFS + nB
|
||||
nW = waves['N']
|
||||
# Generate arrays for positions, areas and normals
|
||||
pos = np.zeros((n, 4), dtype=np.float32)
|
||||
area = np.zeros((n ), dtype=np.float32)
|
||||
normal = np.zeros((n, 4), dtype=np.float32)
|
||||
p = np.zeros((n ), dtype=np.float32)
|
||||
dp = np.zeros((n ), dtype=np.float32)
|
||||
w = np.zeros((nW,4), dtype=np.float32)
|
||||
pos[0:nFS] = fs['pos'].reshape((nFS,4))
|
||||
area[0:nFS] = fs['area'].reshape((nFS))
|
||||
normal[0:nFS] = fs['normal'].reshape((nFS,4))
|
||||
nx = fs['Nx']
|
||||
ny = fs['Ny']
|
||||
p[0:n] = bem['p']
|
||||
dp[0:n] = bem['gradp']
|
||||
w[0:nW] = waves['data']
|
||||
# Create OpenCL objects if not already generated
|
||||
if not self.A:
|
||||
mf = cl.mem_flags
|
||||
self.A = cl.Buffer( self.context, mf.WRITE_ONLY, size = n*n * np.dtype('float32').itemsize )
|
||||
self.B = cl.Buffer( self.context, mf.WRITE_ONLY, size = n * np.dtype('float32').itemsize )
|
||||
self.dB = cl.Buffer( self.context, mf.WRITE_ONLY, size = n * np.dtype('float32').itemsize )
|
||||
self.pos = cl.Buffer( self.context, mf.READ_ONLY, size = n*4 * np.dtype('float32').itemsize )
|
||||
self.area = cl.Buffer( self.context, mf.READ_ONLY, size = n * np.dtype('float32').itemsize )
|
||||
self.normal = cl.Buffer( self.context, mf.READ_ONLY, size = n*4 * np.dtype('float32').itemsize )
|
||||
self.bem_p = cl.Buffer( self.context, mf.READ_ONLY, size = n * np.dtype('float32').itemsize )
|
||||
self.bem_dp = cl.Buffer( self.context, mf.READ_ONLY, size = n * np.dtype('float32').itemsize )
|
||||
self.waves = cl.Buffer( self.context, mf.READ_ONLY, size = nW*4 * np.dtype('float32').itemsize )
|
||||
# Transfer data to buffers
|
||||
events = []
|
||||
events.append(cl.enqueue_write_buffer(self.queue, self.pos, pos))
|
||||
events.append(cl.enqueue_write_buffer(self.queue, self.area, area))
|
||||
events.append(cl.enqueue_write_buffer(self.queue, self.normal, normal))
|
||||
events.append(cl.enqueue_write_buffer(self.queue, self.bem_p, p))
|
||||
events.append(cl.enqueue_write_buffer(self.queue, self.bem_dp, dp))
|
||||
events.append(cl.enqueue_write_buffer(self.queue, self.waves, w))
|
||||
for e in events:
|
||||
e.wait()
|
||||
|
||||
56
src/Mod/Ship/simRun/theory/abstract.tex
Normal file
56
src/Mod/Ship/simRun/theory/abstract.tex
Normal file
|
|
@ -0,0 +1,56 @@
|
|||
\chapter{Introduction}
|
||||
\label{s:introduction}
|
||||
%
|
||||
\section{Objective}
|
||||
%
|
||||
The objective of this document is introduce briefly how the waves of the
|
||||
seakeeping simulator are propagated.\rc
|
||||
%
|
||||
In the seakeeping simulator Boundary Elements Method (BEM) will be used,
|
||||
that is detailed described in several books, like \citet{bem_2007}.
|
||||
\citet{vinayan2007} gives a detailed description of the propagation
|
||||
of waves in a 2D case, and is a good starting point.\rc
|
||||
%
|
||||
We will start briefly describing the governing equations in order to can
|
||||
start working with the 2D problem. First the incident waves over our
|
||||
computational domain will be described, introducing also the potential,
|
||||
discussing then the BEM applied to this case. As we will see the Laplace
|
||||
problem in the 2D case will not be really useful for us.\rc
|
||||
%
|
||||
After that we can start working in the 3D case, that is our real objective.
|
||||
The incident waves will be rewritten, and the Laplace problem and the BEM
|
||||
application purposed again.
|
||||
%
|
||||
\chapter{Governing equations}
|
||||
\label{s:governing_equations}
|
||||
%
|
||||
Assuming no viscous fluid (that allows to transform Navier-Stokes
|
||||
equations into Euler ones), and imposing an initial condition such
|
||||
that\footnote{With no viscous fluid this condition is preserved along the
|
||||
time}:
|
||||
%
|
||||
\begin{eqnarray}
|
||||
\rotational \bs{u} = 0
|
||||
\end{eqnarray}
|
||||
%
|
||||
The fluid velocity derives from a scalar function potential $\phi$
|
||||
%
|
||||
\begin{eqnarray}
|
||||
\label{eq:governing_equations:v_potential}
|
||||
\gradient \phi = \bs{u}
|
||||
\end{eqnarray}
|
||||
%
|
||||
Then the Navier-Stokes equations can be rewriten as a Laplacian problem
|
||||
and Bernoulli equation:
|
||||
%
|
||||
\begin{eqnarray}
|
||||
\label{eq:governing_equations:laplace}
|
||||
\laplacian \phi = & 0
|
||||
\\
|
||||
\label{eq:governing_equations:bernoulli}
|
||||
p = & - \rho \left( \vert \bs{u} \vert^2 + g \bs{z} \right)
|
||||
\end{eqnarray}
|
||||
%
|
||||
And in order to solve the Laplace problem \ref{eq:governing_equations:laplace}
|
||||
we will use the BEM as described by \citet{bem_2007}.
|
||||
%
|
||||
91
src/Mod/Ship/simRun/theory/bib.bib
Normal file
91
src/Mod/Ship/simRun/theory/bib.bib
Normal file
|
|
@ -0,0 +1,91 @@
|
|||
@Comment{THE COMMENTS IN BIBTEX ARE IMPLEMENTED THIS WAY!}
|
||||
@STRING(OE="Ocean Engineering")
|
||||
@STRING{AA = "Astron. Astrophys."}
|
||||
@STRING{ACA = "Extraits des comptes rendus des s\'eances de l'Acad\'emie des Sciences"}
|
||||
@STRING{AG = "Adv. Geophys."}
|
||||
@STRING{AIAAJ = "AIAA J."}
|
||||
@STRING{AIAAP = "AIAA Pap."}
|
||||
@STRING{AMR = "Appl. Mech. Rev."}
|
||||
@STRING{ARFM = "Annu. Rev. Fluid Mech."}
|
||||
@STRING{ARAA = "Annu. Rev. Astron. Astrophy."}
|
||||
@STRING{AMCFD = "Advanced Methods for Computational Fluid Dynamics"}
|
||||
@STRING{AMC = "Applied Mathematics and Computations"}
|
||||
@STRING{ANM = "Applied Numerical Mathematics"}
|
||||
@STRING{BAPS = "Bull. Am. Phys. Soc."}
|
||||
@STRING{CUP = "Cambridge University Press"}
|
||||
@STRING{CMAME = "Comput. Methods Appl. Mech. Engrg."}
|
||||
@STRING{DI = "Dantec Information"}
|
||||
@STRING{EF = "Expts. Fluids"}
|
||||
@STRING{EJMF = "Eur. J. Mech. B/Fluids"}
|
||||
@STRING{IJHFF = "Int. J. Heat and Fluid Flow"}
|
||||
@STRING{IJHMT = "Int. J. Heat and Mass Transfer"}
|
||||
@STRING{IJIE = "Int. J. Impact Engng."}
|
||||
@STRING{IJNMF = "Int. J. Numer. Methods Fluids"}
|
||||
@STRING{INPG = "Institut National Polytechnique Grenoble"}
|
||||
@STRING{JA = "J. Aircraft"}
|
||||
@STRING{JAM = "J. Applied Mech."}
|
||||
@STRING{JAMTP = "J. Appl. Mech. Tech. Phys."}
|
||||
@STRING{JAP = "J. App. Phys."}
|
||||
@STRING{JAS = "J. Atmos. Sci."}
|
||||
@STRING{JCP = "J. Comp. Phys."}
|
||||
@STRING{JCAM = "J. Computational and Applied Mathematics"}
|
||||
@STRING{JFE = "J. Fluids Engine."}
|
||||
@STRING{JFM = "J. Fluid Mech."}
|
||||
@STRING{JHE = "J. Hydraulic Engineering"}
|
||||
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src/Mod/Ship/simRun/theory/laplace2D.tex
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src/Mod/Ship/simRun/theory/laplace2D.tex
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|
|
@ -0,0 +1,196 @@
|
|||
\chapter{Waves propagations in 2D plane}
|
||||
\label{s:laplace2D}
|
||||
%
|
||||
\section{General}
|
||||
%
|
||||
In this chapter the 2D case will be discussed, looking for
|
||||
a method to solve the BEM using only the information about
|
||||
the free surface. As we will see is not possible to do it in
|
||||
the 2D case, and may move to 3D case.
|
||||
%
|
||||
\section{Incident waves}
|
||||
%
|
||||
First for all we need to describe the incident waves, that are
|
||||
the waves out of our computational domain.
|
||||
%
|
||||
\begin{eqnarray}
|
||||
\label{eq:laplace2D:incident_waves}
|
||||
\begin{array}{rcl}
|
||||
z(x,t) & = & \dsty{\sum_{j=1}^{n_{waves}}} a_j \sin\left(k_j x - \omega_j t + \delta_j \right)
|
||||
\\
|
||||
v_z(x,t) & = & \dsty{\sum_{j=1}^{n_{waves}}} - a_j \omega_j \cos\left(k_j x - \omega_j t + \delta_j \right)
|
||||
\end{array}
|
||||
\end{eqnarray}
|
||||
%
|
||||
The phase velocity for the waves in the most general case can
|
||||
be written as:
|
||||
%
|
||||
\begin{eqnarray}
|
||||
\label{eq:laplace2D:c_general}
|
||||
c_j = \sqrt{\frac{g \lambda}{2 \pi} \tanh\left(\frac{2 \pi d}{\lambda}\right)}
|
||||
\end{eqnarray}
|
||||
%
|
||||
But if the water depth is such that $d > \frac{\lambda}{2}$ we
|
||||
can rewrite the phase velocity \ref{eq:laplace2D:c_general} as
|
||||
%
|
||||
\begin{eqnarray}
|
||||
\label{eq:laplace2D:c_deep}
|
||||
c_j^{deep} = \sqrt{\frac{g \lambda}{2 \pi}}
|
||||
\end{eqnarray}
|
||||
%
|
||||
By definition the phase velocity can be also written as
|
||||
$c_j = \omega_j / k_j$, so we can relate the wave length
|
||||
with the period
|
||||
%
|
||||
\begin{eqnarray}
|
||||
\label{eq:laplace2D:k_w}
|
||||
k_j = \frac{\omega_j^2}{g}
|
||||
\end{eqnarray}
|
||||
%
|
||||
Regarding the velocity potential, let us define it as
|
||||
%
|
||||
\begin{eqnarray}
|
||||
\label{eq:laplace2D:incident_waves_potential}
|
||||
\phi(x,z,t) = \sum_{j=1}^{n_{waves}} - \frac{a_j \omega_j}{k_j}
|
||||
\cos\left(k_j x - \omega_j t + \delta_j \right)
|
||||
\exp\left(k_j z\right)
|
||||
\end{eqnarray}
|
||||
%
|
||||
such that
|
||||
%
|
||||
\begin{eqnarray*}
|
||||
\begin{array}{rcl}
|
||||
\dsty{\left. \frac{\partial \phi(x,z,t)}{\partial z} \right\vert_{z=0}} & = & v_z(x,t)
|
||||
\\
|
||||
\laplacian \phi(x,z,t) & = & 0
|
||||
\end{array}
|
||||
\end{eqnarray*}
|
||||
%
|
||||
This potential is valid for deep water waves if the exponent
|
||||
$k_j z$ is small enough. $z$ can take values of the order of
|
||||
$\mathcal{O}(a_j)$, so this method is valid for waves which
|
||||
the length is such that
|
||||
%
|
||||
\begin{eqnarray*}
|
||||
\lambda_j \gg 2 \pi a_j
|
||||
\end{eqnarray*}
|
||||
%
|
||||
\section{BEM applied to Laplace 2D problem}
|
||||
\label{ss:laplace2D:bem}
|
||||
%
|
||||
We have defined the sea waves outside from our computational domain
|
||||
$\Omega$, where the waves can be perturbed by floating objects. In
|
||||
the figure \ref{fig:ss:laplace2D:bem} a schematic view of the
|
||||
computational domain is shown.\rc
|
||||
%
|
||||
The BEM is based in the reciprocal relation application
|
||||
%
|
||||
\begin{eqnarray}
|
||||
\label{eq:laplace2D:reciprocal_relation}
|
||||
\lambda(X, Z) \phi(X, Z; t) = \int_{\partial \Omega}
|
||||
\phi(x, z; t) \frac{\partial G(x, z, X, Z)}{\partial \bs{n}(x, z)} -
|
||||
G(x, z, X, Z) \frac{\partial \phi(x, z; t)}{\partial \bs{n}(x, z)}
|
||||
\mbox{d} s(x, z)
|
||||
\end{eqnarray}
|
||||
%
|
||||
Where
|
||||
%
|
||||
\begin{eqnarray*}
|
||||
\lambda(X, Z) = \left\lbrace
|
||||
\begin{array}{lcl}
|
||||
1 & \mbox{if} & (X, Z) \in \Omega
|
||||
\\
|
||||
\frac{1}{2} & \mbox{if} & (X, Z) \in \partial \Omega
|
||||
\\
|
||||
0 & \mbox{if} & (X, Z) \not \in \Omega
|
||||
\end{array}
|
||||
\right.
|
||||
\end{eqnarray*}
|
||||
%
|
||||
$G(x, z, X, Z)$ is the Green's function (a particular solution
|
||||
of the Laplace equation), and the derivative respect to normal
|
||||
denotes the gradient of the function projected over the normal.
|
||||
%
|
||||
\begin{eqnarray*}
|
||||
\frac{\partial f(x, z)}{\partial \bs{n}(x, z)} =
|
||||
\gradient f(x, z) \cdot \bs{n}(x, z)
|
||||
\end{eqnarray*}
|
||||
%
|
||||
Hereinafter let we define the function $H(x, z, X, Z)$ as
|
||||
%
|
||||
\begin{eqnarray*}
|
||||
H(x, z, X, Z) = \frac{\partial G(x, z, X, Z)}{\partial \bs{n}(x, z)}
|
||||
\end{eqnarray*}
|
||||
%
|
||||
Therefore BEM allows to, knowing along the contour the potential or
|
||||
the gradient, not both, compute the another one. The parts of the
|
||||
contour where we know both potential and the gradient will enter in
|
||||
the method as part of the independent term in the linear system of
|
||||
equations.\rc
|
||||
%
|
||||
Since we know the potential out from the domain $\Omega$, we can know
|
||||
the potential and the gradient along the inlet $\partial \Omega_{Inlet}$
|
||||
and outlet $\partial \Omega_{Outlet}$.\rc
|
||||
%
|
||||
Regarding the bottom, we only can assert that the gradient along the
|
||||
normal, that is the vertical velocity of the fluid, is null.\rc
|
||||
%
|
||||
Therefore, the inlet and outlet have relatively good properties because
|
||||
we know all the data, so will not be additional work into the linear
|
||||
system matrix that must be inverted, but the bottom don't have this
|
||||
desirable property.\rc
|
||||
%
|
||||
Nevertheless, since the geometry of the inlet and
|
||||
outlet is different from the free surface, and the bottom must be
|
||||
explicitly considered, all the contour must be discretized with an
|
||||
undesirable computational cost associated.\rc
|
||||
%
|
||||
So we are interested to know if we can replace our computational
|
||||
domain $\Omega$ for other where only the free surface contour is
|
||||
involved, moving the Inlet, the Outlet, and the bottom infinity far. We
|
||||
could change our computational domain if the Green's function, and their
|
||||
gradient, goes to zero as we go far enough. In 2D we can found a Green's
|
||||
function for the Laplace problem such that
|
||||
%
|
||||
\begin{eqnarray}
|
||||
\label{eq:laplace2D:g}
|
||||
G(x, z, X, Z) = & \dsty{\frac{1}{4 \pi}} \log \left( \left(x - X\right)^2 + \left(z - Z\right)^2 \right)
|
||||
\\
|
||||
\label{eq:laplace2D:h}
|
||||
H(x, z, X, Z) = & \dsty{\frac{1}{2 \pi}} \frac{\left( x - X, z - Z \right)}{\left( \left(x - X\right)^2 + \left(z - Z\right)^2 \right)}
|
||||
\end{eqnarray}
|
||||
%
|
||||
Whose limits when the radius goes to infinite can be found
|
||||
%
|
||||
\begin{eqnarray}
|
||||
\label{eq:laplace2D:limit_g}
|
||||
\lim_{(x-X)^2 + (z-Z)^2 \to \infty} G(x, z, X, Z) = & \infty
|
||||
\\
|
||||
\label{eq:laplace2D:limit_h}
|
||||
\lim_{(x-X)^2 + (z-Z)^2 \to \infty} H(x, z, X, Z) = & 0
|
||||
\end{eqnarray}
|
||||
%
|
||||
So in the 2D Laplace problem, if we try to send the Inlet, the Outlet,
|
||||
or the bottom to the infinite we can't use BEM because the Green's
|
||||
function is not well defined, diverging with the distance.
|
||||
%
|
||||
\begin{figure}[ht!]
|
||||
\centering
|
||||
\includegraphics[width=0.4\textwidth]{Omega}
|
||||
\caption{Computational domain $\Omega$}
|
||||
\label{fig:ss:laplace2D:bem}
|
||||
\end{figure}
|
||||
%
|
||||
\section{Conclusions to Laplace 2D problem}
|
||||
\label{ss:laplace2D:conclusions}
|
||||
%
|
||||
We have briefly discussed the wave propagation problem using BEM in a 2D
|
||||
case, seeing that in this case we need to consider all the contours,
|
||||
including the Inlet, the Outlet, and the bottom. This approach is
|
||||
successfully applied in a 2D problem in the reference \citep{vinayan2007}.
|
||||
In 2D problem considering all the contours is not a heavy problem because
|
||||
the number of nodes is usually small compared with a 3D case, but in a 3D
|
||||
problem a computational less expensive method is required.\rc
|
||||
%
|
||||
We will not continue with the 2D Laplace problem because the solution will
|
||||
not be useful for us in the 3D case.
|
||||
642
src/Mod/Ship/simRun/theory/laplace3D.tex
Normal file
642
src/Mod/Ship/simRun/theory/laplace3D.tex
Normal file
|
|
@ -0,0 +1,642 @@
|
|||
\chapter{Waves propagations in 3D}
|
||||
\label{s:laplace3D}
|
||||
%
|
||||
\section{General}
|
||||
%
|
||||
In this chapter the 3D case will be discussed, looking for
|
||||
a method to solve the BEM using only the information about
|
||||
the free surface.
|
||||
%
|
||||
This case is our main objective in order to can setup 6-DOF
|
||||
seakeeping simulations.
|
||||
%
|
||||
\section{Incident waves}
|
||||
%
|
||||
We can rewrite the sea waves system outside from our
|
||||
computational domain $\Omega$
|
||||
%
|
||||
\begin{eqnarray}
|
||||
\label{eq:laplace3D:incident_waves}
|
||||
\begin{array}{rcl}
|
||||
z(x,y,t) & = & \dsty{\sum_{j=1}^{n_{waves}}} a_j \sin\left(k_j \left(x \cos(\beta) + y \sin(\beta)\right) - \omega_j t + \delta_j \right)
|
||||
\\
|
||||
v_z(x,y,t) & = & \dsty{\sum_{j=1}^{n_{waves}}} - a_j \omega_j \cos\left(k_j \left(x \cos(\beta) + y \sin(\beta)\right) - \omega_j t + \delta_j \right)
|
||||
\\
|
||||
\phi(x,z,t) & = & \dsty{\sum_{j=1}^{n_{waves}}} - \frac{a_j \omega_j}{k_j}
|
||||
\cos\left(k_j \left(x \cos(\beta) + y \sin(\beta)\right) - \omega_j t + \delta_j \right)
|
||||
\exp\left(k_j z\right)
|
||||
\\
|
||||
k_j & = & \dsty{\frac{\omega_j^2}{g}}
|
||||
\end{array}
|
||||
\end{eqnarray}
|
||||
%
|
||||
Where $\beta$ is the heading angle, being 0 for stern waves. For
|
||||
this wave system still being valid the phase velocity from the
|
||||
equation \ref{eq:laplace2D:c_deep}. The purposed potential is
|
||||
compatible with the Laplace equation
|
||||
\ref{eq:governing_equations:laplace} as well.
|
||||
%
|
||||
\section{BEM applied to Laplace 3D problem}
|
||||
\label{ss:laplace3D:bem}
|
||||
%
|
||||
\subsection{Computational domain}
|
||||
\label{sss:laplace3D:computational_domain}
|
||||
%
|
||||
We have a domain similar to the shown in the figure
|
||||
\ref{fig:ss:laplace2D:bem}, but in this case 2 more boundaries
|
||||
must be considered in the missed direction, that we will call
|
||||
$\partial \Omega_{Front}$ and $\partial \Omega_{Back}$. As in
|
||||
the 2D case we will apply the reciprocal relation
|
||||
%
|
||||
\begin{eqnarray}
|
||||
\label{eq:laplace3D:reciprocal_relation}
|
||||
\lambda(X, Y, Z) \phi(X, Y, Z; t) = \int_{\partial \Omega}
|
||||
\phi(x, y, z; t) \frac{\partial G(x, y, z, X, Y, Z)}{\partial \bs{n}(x, y, z)} -
|
||||
G(x, y, z, X, Y, Z) \frac{\partial \phi(x, y, z; t)}{\partial \bs{n}(x, y, z)}
|
||||
\mbox{d} s(x, y, z)
|
||||
\end{eqnarray}
|
||||
%
|
||||
We are focused into compute the gradient of the velocity
|
||||
potential along the free surface knowing the velocity
|
||||
potential value in each point one. Let we define the
|
||||
function $H(x,y,z,X,Y,Z)$ again
|
||||
%
|
||||
\begin{eqnarray*}
|
||||
H(x, y, z, X, Y, Z) = \frac{\partial G(x, y, z, X, Y, Z)}{\partial \bs{n}(x, y, z)}
|
||||
\end{eqnarray*}
|
||||
%
|
||||
As in the Laplace equation for the 2D case, described in the
|
||||
chapter \ref{s:laplace2D}, we want to expand the domain $\Omega$
|
||||
such that all the boundaries except the free surface will the
|
||||
infinity far, adding the boundary $\partial \Omega_{FS,I}$, where
|
||||
we know the velocity potential and their gradient from
|
||||
\ref{eq:laplace3D:incident_waves}. In the figure
|
||||
\ref{fig:ss:laplace3D:bem} a schematic view of the expanded
|
||||
domain can be seen.\rc
|
||||
%
|
||||
The main advantage is that, as happens with the Inlet and the
|
||||
Outlet, we know all the needed data about the velocity potential,
|
||||
so we can significantly reduce the linear system matrix dimensions,
|
||||
and as happens with the bottom, the geometry is so quite similar
|
||||
to the $\Omega_{FS}$ one, so no additional discretization or memory
|
||||
storage is needed.\rc
|
||||
%
|
||||
This trick will only works if the Green's function $G(x,y,z,X,Y,Z)$,
|
||||
and their gradient $H(x,y,z,X,Y,Z)$, goes to zero as $(x,y,z)$ goes
|
||||
to infinite. In 3D Laplace problems we can use the following Green's
|
||||
function:
|
||||
%
|
||||
\begin{eqnarray}
|
||||
\label{eq:laplace3D:g}
|
||||
G(x,y,z,X,Y,Z) = & \dsty{\frac{1}{\sqrt{\left(x - X\right)^2 + \left(y - Y\right)^2 + \left(z - Z\right)^2}}}
|
||||
\\
|
||||
\label{eq:laplace3D:h}
|
||||
H(x,y,z,X,Y,Z) = & - \dsty{\frac{\left( x - X, y - Y, z - Z \right)}{\left(\left(x - X\right)^2 + \left(y - Y\right)^2 + \left(z - Z\right)^2\right)^{3/2}}}
|
||||
\end{eqnarray}
|
||||
%
|
||||
That in the limit
|
||||
%
|
||||
\begin{eqnarray}
|
||||
\label{eq:laplace3D:limit_g}
|
||||
\lim_{(x-X)^2 + (y-Y)^2 + (z-Z)^2 \to \infty} G(x,y,z,X,Y,Z) = & 0
|
||||
\\
|
||||
\label{eq:laplace3D:limit_h}
|
||||
\lim_{(x-X)^2 + (y-Y)^2 + (z-Z)^2 \to \infty} H(x,y,z,X,Y,Z) = & 0
|
||||
\end{eqnarray}
|
||||
%
|
||||
So in this case, if the potential of the incidents waves is
|
||||
a good function along all the free surface we can move from
|
||||
the domain shown in the figure \ref{fig:ss:laplace2D:bem} to
|
||||
the shown in the figure \ref{fig:ss:laplace3D:bem}, due to
|
||||
along the other boundaries the Green's functions $G(x,y,z,X,Y,Z)$
|
||||
and $H(x,y,z,X,Y,Z)$ are nulls, not computing in the equation
|
||||
\ref{eq:laplace2D:reciprocal_relation}.
|
||||
%
|
||||
\begin{figure}[ht!]
|
||||
\centering
|
||||
\includegraphics[width=0.6\textwidth]{Omega2}
|
||||
\caption{Computational domain $\Omega$}
|
||||
\label{fig:ss:laplace3D:bem}
|
||||
\end{figure}
|
||||
%
|
||||
\subsection{Boundary conditions (BC)}
|
||||
\label{sss:laplace3D:BC}
|
||||
%
|
||||
In order to can purpose an evolution process we need to use
|
||||
the boundary conditions along the free surface. In the most
|
||||
general way we can rewrite the Bernoulli equation, that is
|
||||
the dynamic free surface boundary condition (DFSBC), as (see
|
||||
\citep{yang2004}):
|
||||
%
|
||||
\begin{eqnarray}
|
||||
\label{eq:laplace3D:FS_Bernoulli}
|
||||
\frac{\mbox{D} \phi(x,y,z;t)}{\mbox{D} t} =
|
||||
\frac{1}{2}\left\vert \gradient \phi \right\vert^2
|
||||
- g z(x,y;t)
|
||||
- \frac{p_0}{\rho}
|
||||
- \bs{U}(t) \cdot \gradient \phi(x,y,z;t)
|
||||
- \frac{\partial \bs{U}(t)}{\partial t} \cdot (x,y,0)
|
||||
\end{eqnarray}
|
||||
%
|
||||
Where $p_0$ is the atmospheric pressure, that we will consider
|
||||
null, and $\bs{U}(t)$ is the ship velocity, in this case will be
|
||||
a null vector. Since the material derivative denotes
|
||||
%
|
||||
\begin{eqnarray*}
|
||||
\frac{\mbox{D} f}{\mbox{D} t} =
|
||||
\frac{\partial f}{\partial t}
|
||||
\gradient{\phi(x,y,z;t)} \cdot \gradient{f}
|
||||
\end{eqnarray*}
|
||||
%
|
||||
We can rewrite the dynamic boundary condition for this specific case as
|
||||
%
|
||||
\begin{eqnarray}
|
||||
\label{eq:laplace3D:DFSBC}
|
||||
\frac{\partial \phi(x,y,z;t)}{\partial t} =
|
||||
- \frac{1}{2}\left\vert \gradient \phi \right\vert^2
|
||||
- g z(x,y;t)
|
||||
\end{eqnarray}
|
||||
%
|
||||
Regarding the kinematic free surface boundary condition (KFSBC), in the
|
||||
most general way we can write that
|
||||
%
|
||||
\begin{eqnarray}
|
||||
\label{eq:laplace3D:FS_Kinematic}
|
||||
\frac{\mbox{D} z(x,y;t)}{\mbox{D} t} =
|
||||
\frac{\partial \phi(x,y,z;t)}{\partial z}
|
||||
- \bs{U}(t) \cdot \gradient z(x,y;t)
|
||||
\end{eqnarray}
|
||||
%
|
||||
Where we can expand the material derivative, writing the KFSBC for this
|
||||
specific case
|
||||
%
|
||||
\begin{eqnarray}
|
||||
\label{eq:laplace3D:KFSBC}
|
||||
\frac{\partial z(x,y;t)}{\partial t} =
|
||||
\frac{\partial \phi(x,y,z;t)}{\partial z}
|
||||
- \gradient{\phi(x,y,z;t)} \cdot \gradient{z(x,y;t)}
|
||||
\end{eqnarray}
|
||||
%
|
||||
\subsection{Time integration scheme}
|
||||
\label{sss:laplace3D:TimeIntegration}
|
||||
%
|
||||
We may start the simulation in a initial condition where we know the
|
||||
full free surface shape and velocity potential, including the gradients.
|
||||
%
|
||||
\begin{eqnarray}
|
||||
\label{eq:laplace3D:IC}
|
||||
\begin{array}{lcl}
|
||||
z(x,y;t=0) & = & z_0(x,y)
|
||||
\\
|
||||
\phi(x,y,z;t=0) & = & \phi_0(x,y,z)
|
||||
\\
|
||||
\gradient z(x,y;t=0) & = & \gradient z_0(x,y)
|
||||
\\
|
||||
\gradient \phi(x,y,z;t=0) & = & \gradient \phi_0(x,y,z)
|
||||
\end{array}
|
||||
\end{eqnarray}
|
||||
%
|
||||
In the computational part of the free surface is enough to know the free
|
||||
surface shape $z_0(x,y)$ and the velocity potential $\phi_0(x,y,z)$.\rc
|
||||
%
|
||||
For simplicity we will use an Euler's integration scheme, but the same
|
||||
method can be easily applied for any other explicit time integrator, like
|
||||
the Adams-Bashforth ones.\rc
|
||||
%
|
||||
In each time step we start knowing the shape of the free surface, and the
|
||||
velocity potential, and basically we want to compute these fields for the
|
||||
next time step. To do it the following steps are followed:
|
||||
%
|
||||
\begin{enumerate}
|
||||
\item We use BEM to compute the velocity potential gradient, as will be
|
||||
described in the section \ref{sss:laplace3D:bem_solve}.
|
||||
\begin{eqnarray}
|
||||
\label{eq:laplace3D:time_march:bem}
|
||||
\gradient{\phi(x,y,z;t)} = \mbox{BEM}\left(\phi(x,y,z;t), z(x,y;t)\right)
|
||||
\end{eqnarray}
|
||||
\item We use the KFSBC to compute the derivative of the free surface
|
||||
elevation, and the DFSBC to know the derivative of the velocity potential.
|
||||
\begin{eqnarray}
|
||||
\label{eq:laplace3D:time_march:dzdt}
|
||||
\frac{\partial z(x,y;t)}{\partial t} = &
|
||||
\mbox{KFSBC}\left(\gradient{\phi(x,y,z;t)}\right)
|
||||
\\
|
||||
\label{eq:laplace3D:time_march:dphidt}
|
||||
\frac{\partial \phi(x,y,z;t)}{\partial t} = &
|
||||
\mbox{DFSBC}\left(z(x,y;t), \gradient{\phi(x,y,z;t)}\right)
|
||||
\end{eqnarray}
|
||||
\item And then we can perform the time integration.
|
||||
\begin{eqnarray}
|
||||
\label{eq:laplace3D:time_march:z_integrate}
|
||||
z(x,y;t + \Delta t) = &
|
||||
z(x,y;t) +
|
||||
\Delta t \dsty \frac{\partial z(x,y;t)}{\partial t}
|
||||
\\
|
||||
\label{eq:laplace3D:time_march:phi_integrate}
|
||||
\phi(x,y,z;t + \Delta t) = &
|
||||
\phi(x,y,z;t + \Delta t) +
|
||||
\Delta t \dsty \frac{\partial \phi(x,y,z;t)}{\partial t}
|
||||
\end{eqnarray}
|
||||
\end{enumerate}
|
||||
%
|
||||
\subsection{Discrete Laplace solution using the BEM}
|
||||
\label{sss:laplace3D:bem_solve}
|
||||
%
|
||||
As we have seen in the previous sections we want to use the BEM in order
|
||||
to compute the velocity potential gradient in the free surface from the
|
||||
velocity potential value known. In the equation
|
||||
\ref{eq:laplace3D:reciprocal_relation} we can starting dividing the domain
|
||||
contour as shown in the figure \ref{fig:ss:laplace3D:bem}, getting the
|
||||
computational one, denoted by $\partial \Omega_{FS}$, and
|
||||
the extension one, denoted by $\partial \Omega_{FS,I}$, where the free
|
||||
surface and the velocity potential and gradient is known for all the
|
||||
time instants.
|
||||
%
|
||||
\begin{eqnarray}
|
||||
\label{eq:laplace3D:reciprocal_relation:002}
|
||||
\begin{array}{l}
|
||||
\frac{1}{2} \phi(X, Y, Z; t) =
|
||||
\\
|
||||
\dsty \int_{\partial \Omega_{FS}}
|
||||
\phi(x, y, z; t) \frac{\partial G(x, y, z, X, Y, Z)}{\partial \bs{n}(x, y, z)} -
|
||||
G(x, y, z, X, Y, Z) \frac{\partial \phi(x, y, z; t)}{\partial \bs{n}(x, y, z)}
|
||||
\mbox{d} s(x, y, z)
|
||||
\\
|
||||
\dsty \int_{\partial \Omega_{FS,I}}
|
||||
\phi(x, y, z; t) \frac{\partial G(x, y, z, X, Y, Z)}{\partial \bs{n}(x, y, z)} -
|
||||
G(x, y, z, X, Y, Z) \frac{\partial \phi(x, y, z; t)}{\partial \bs{n}(x, y, z)}
|
||||
\mbox{d} s(x, y, z)
|
||||
\end{array}
|
||||
\end{eqnarray}
|
||||
%
|
||||
Where we already assumed that $(x,y,z) \in \partial \Omega$. We can start discretizing
|
||||
the velocity potential, assuming that the potential and their gradient changes smoothly
|
||||
enough. The our contours can be divided according to the grid:
|
||||
%
|
||||
\begin{eqnarray}
|
||||
\label{eq:laplace3D:reciprocal_relation:003}
|
||||
\begin{array}{rl}
|
||||
\frac{1}{2} \phi_a = &
|
||||
\dsty \sum_{b=1}^{n_{FS}}
|
||||
\phi_b
|
||||
\dsty \int_{\partial \Omega_{FS}^b} H(\bs{x}, \bs{x}_a) \mbox{d} s(\bs{x})
|
||||
-
|
||||
\dsty \sum_{b=1}^{n_{FS}}
|
||||
\frac{\partial \phi_b}{\partial \bs{n}_b}
|
||||
\dsty \int_{\partial \Omega_{FS}^b} G(\bs{x}, \bs{x}_a) \mbox{d} s(\bs{x})
|
||||
\\
|
||||
&
|
||||
\dsty \sum_{b=1}^{n_{FS,I}}
|
||||
\phi_b
|
||||
\dsty \int_{\partial \Omega_{FS,I}^b} H(\bs{x}, \bs{x}_a) \mbox{d} s(\bs{x})
|
||||
-
|
||||
\dsty \sum_{b=1}^{n_{FS,I}}
|
||||
\frac{\partial \phi_b}{\partial \bs{n}_b}
|
||||
\dsty \int_{\partial \Omega_{FS,I}^b} G(\bs{x}, \bs{x}_a) \mbox{d} s(\bs{x})
|
||||
\end{array}
|
||||
\end{eqnarray}
|
||||
%
|
||||
The functions $G(x,y,z,X,Y,Z)$ and $H(x,y,z,X,Y,Z)$, according to the equations
|
||||
\ref{eq:laplace3D:g} and \ref{eq:laplace3D:h}, are well defined in all the
|
||||
subintervals where $(x,y,z) \neq (X,Y,Z)$, and are so quite smooth, so we will
|
||||
change all the integrals that accomplish it for point evaluations.
|
||||
%
|
||||
\begin{eqnarray}
|
||||
\label{eq:laplace3D:reciprocal_relation:004}
|
||||
\begin{array}{rl}
|
||||
\frac{1}{2} \phi_a = &
|
||||
\phi_a
|
||||
\dsty \int_{\partial \Omega_{FS}^a} H(\bs{x}, \bs{x}_a) \mbox{d} s(\bs{x})
|
||||
-
|
||||
\frac{\partial \phi_a}{\partial \bs{n}_a}
|
||||
\dsty \int_{\partial \Omega_{FS}^a} G(\bs{x}, \bs{x}_a) \mbox{d} s(\bs{x})
|
||||
\\
|
||||
&
|
||||
\dsty \sum_{\substack{b = 1 \\ b \neq a}}^{n_{FS}}
|
||||
\left(
|
||||
\phi_b H_{ba} - \frac{\partial \phi_b}{\partial \bs{n}_b} G_{ba}
|
||||
\right) S_b
|
||||
+
|
||||
\dsty \sum_{b=1}^{n_{FS,I}}
|
||||
\left(
|
||||
\phi_b H_{ba} - \frac{\partial \phi_b}{\partial \bs{n}_b} G_{ba}
|
||||
\right) S_b
|
||||
\end{array}
|
||||
\end{eqnarray}
|
||||
%
|
||||
The remaining integrals must be treated carefully since the functions are
|
||||
singular in the center of the interval. $H(x,y,z,X,Y,Z)$ is an odd function,
|
||||
so the limit of the integral when the radius of the interval goes to zero
|
||||
is null, being well defined. Regarding the function $G(x,y,z,X,Y,Z)$ is an
|
||||
even function of order:
|
||||
%
|
||||
\begin{eqnarray*}
|
||||
G(\bs{x},\bs{x_a}) = \mathcal{O}\left(\frac{1}{\vert \bs{x} - \bs{x_a}\vert}\right)
|
||||
\end{eqnarray*}
|
||||
%
|
||||
Which their integral is defined if the function $z(x,y)$ is well defined
|
||||
as well. So the remaining integrals can be numerically computed, being mindful
|
||||
that:
|
||||
%
|
||||
\begin{enumerate}
|
||||
\item Can't be evaluated at the point $\bs{x_a}$.
|
||||
\item Changes too fast around the point $\bs{x_a}$.
|
||||
\end{enumerate}
|
||||
%
|
||||
We will discuss later how to solve this integrals, for the moment we will define
|
||||
new functions such that:
|
||||
%
|
||||
\begin{eqnarray}
|
||||
\label{eq:laplace3D:g:hat}
|
||||
\hat G_{ab} =
|
||||
\left\lbrace \begin{array}{l}
|
||||
\dsty \int_{\partial \Omega_{FS}^a} G(\bs{x}, \bs{x}_a) \mbox{d} s(\bs{x}); \, \, \mbox{if} \, a = b
|
||||
\\
|
||||
G(\bs{x_b},\bs{x_a}) S_b; \, \, \mbox{if} \, a \neq b
|
||||
\end{array} \right.
|
||||
\\
|
||||
\label{eq:laplace3D:h:hat}
|
||||
\hat H_{ab} =
|
||||
\left\lbrace \begin{array}{l}
|
||||
\dsty \int_{\partial \Omega_{FS}^a} H(\bs{x}, \bs{x}_a) \mbox{d} s(\bs{x}); \, \, \mbox{if} \, a = b
|
||||
\\
|
||||
H(\bs{x_b},\bs{x_a}) S_b; \, \, \mbox{if} \, a \neq b
|
||||
\end{array} \right.
|
||||
\end{eqnarray}
|
||||
%
|
||||
So we can rewrite the equation \ref{eq:laplace3D:reciprocal_relation:004}
|
||||
%
|
||||
\begin{eqnarray}
|
||||
\label{eq:laplace3D:reciprocal_relation:005}
|
||||
\frac{1}{2} \phi_a
|
||||
=
|
||||
\dsty \sum_{b=1}^{n_{FS}}
|
||||
\left(
|
||||
\phi_b \hat H_{ba} - \frac{\partial \phi_b}{\partial \bs{n}_b} \hat G_{ba}
|
||||
\right)
|
||||
+
|
||||
\dsty \sum_{b=1}^{n_{FS,I}}
|
||||
\left(
|
||||
\phi_b \hat H_{ba} - \frac{\partial \phi_b}{\partial \bs{n}_b} \hat G_{ba}
|
||||
\right)
|
||||
\end{eqnarray}
|
||||
%
|
||||
Where we can move all the terms of the computational free surface that affects
|
||||
to the gradient of the velocity potential (that is the value that we want to
|
||||
compute) to left hand side, and let all the other ones in the right hand side
|
||||
of the equation
|
||||
%
|
||||
\begin{eqnarray}
|
||||
\label{eq:laplace3D:reciprocal_relation:006}
|
||||
\dsty \sum_{b \in \partial \Omega_{FS}}
|
||||
\frac{\partial \phi_b}{\partial \bs{n}_b} \hat G_{ba}
|
||||
=
|
||||
-
|
||||
\frac{1}{2} \phi_a
|
||||
+
|
||||
\dsty \sum_{b \in \partial \Omega_{FS}}
|
||||
\phi_b \hat H_{ba}
|
||||
+
|
||||
\dsty \sum_{b \in \partial \Omega_{FS,I}}
|
||||
\left(
|
||||
\phi_b \hat H_{ba} -
|
||||
\frac{\partial \phi_b}{\partial \bs{n}_b} \hat G_{ba}
|
||||
\right)
|
||||
\end{eqnarray}
|
||||
%
|
||||
The equation \ref{eq:laplace3D:reciprocal_relation:006}, that
|
||||
has been written for the velocity potential at one point $\bs{x}_a$,
|
||||
can be written for all the points of the free surface along
|
||||
the computational domain using the matrix notation
|
||||
%
|
||||
\begin{eqnarray}
|
||||
\label{eq:laplace3D:reciprocal_relation:007}
|
||||
\mathcal{G} \left[ \frac{ \partial \phi}{\partial \bs{n}} \right]
|
||||
=
|
||||
\left( \mathcal{H} - \frac{1}{2} \mathcal{I} \right) \left[ \phi \right]
|
||||
+
|
||||
\mathcal{H}_{FS,I} \left[ \phi \right]_{FS,I}
|
||||
-
|
||||
\mathcal{G}_{FS,I} \left[ \frac{ \partial \phi}{\partial \bs{n}} \right]_{FS,I}
|
||||
\end{eqnarray}
|
||||
%
|
||||
Note that the area of the elements $S_b$ has been included into
|
||||
the matrices. The equation
|
||||
\ref{eq:laplace3D:reciprocal_relation:007} is a linear system
|
||||
of equations that can be numerically solved, either inverting
|
||||
the matrix, or using an iterative method. The matrix inversion
|
||||
is probably the best way for linear seakeeping codes, where the
|
||||
same matrix will be ever used, but in this case the iterative
|
||||
method is the faster way.\rc
|
||||
%
|
||||
The method described along this section allows to us to compute
|
||||
the gradient of the velocity potential along the free surface
|
||||
knowing the potential in the computational free surface, and both
|
||||
velocity potential and the gradient along the extended free
|
||||
surface.
|
||||
%
|
||||
\subsection{Integrals computation}
|
||||
\label{sss:laplace3D:integrals}
|
||||
%
|
||||
In the equations \ref{eq:laplace3D:g:hat} and \ref{eq:laplace3D:g:hat}
|
||||
we have introduced two inconvenient integrals. Even though the functions
|
||||
are not well defined when $\bs{x} = \bs{x_a}$, their integrals it is.
|
||||
For instance, if we can assume that the free surface is fully planar
|
||||
($z = 0$), the integrals can be analytically computed
|
||||
%
|
||||
\begin{eqnarray*}
|
||||
\dsty \int_{y_a - \delta y}^{y_a + \delta y} \int_{x_a - \delta x}^{x_a + \delta x}
|
||||
G(x,y,0,x_a,y_a,0)
|
||||
\, \mbox{d}x \, \mbox{d}y
|
||||
= &
|
||||
\dsty \frac{
|
||||
\delta x \, \, \mbox{asinh}\left(\frac{\delta y}{\delta x}\right)
|
||||
+
|
||||
\delta y \, \, \mbox{asinh}\left(\frac{\delta x}{\delta y}\right)
|
||||
}{\pi}
|
||||
\\
|
||||
\dsty \int_{y_a - \delta y}^{y_a + \delta y} \int_{x_a - \delta x}^{x_a + \delta x}
|
||||
H(x,y,0,x_a,y_a,0)
|
||||
\, \mbox{d}x \, \mbox{d}y
|
||||
= &
|
||||
0
|
||||
\end{eqnarray*}
|
||||
%
|
||||
But can not be analytically computed for every function $z(x,y)$, being
|
||||
necessary to compute it in a numerical way.\rc
|
||||
%
|
||||
In the figure \ref{fig:ss:laplace3D:integral} a schematic representation
|
||||
of the integration method is shown. Let we want to compute the integral
|
||||
for an element of the grid $(x_a,y_a)$, then we subdivide the element in
|
||||
\textbf{a even number} of subelements of area $dx \cdot dy$, so we can
|
||||
assert that any subelement will be evaluated in the point $(x_a,y_a)$,
|
||||
but as near as we want because we can ever add more subelements; then we
|
||||
can numerically approximate the integral by (here in after we will use
|
||||
only the function $G(\bs{x}, bs{x_a})$, because same method can be applied
|
||||
to the function $H(\bs{x}, bs{x_a})$).
|
||||
%
|
||||
\begin{eqnarray}
|
||||
\label{eq:laplace3D:integral:g}
|
||||
\dsty \int_{\partial \Omega_{FS}^a} G(\bs{x}, \bs{x}_a) \mbox{d} s(\bs{x})
|
||||
\simeq
|
||||
\sum_{i=1}^{n_x} \sum_{j=1}^{n_y} G(x_i,y_j,z(x_i,y_i), x_a, y_a, z(x_a, y_a)) \, dx \, dy
|
||||
\end{eqnarray}
|
||||
%
|
||||
Of course the value $z(x_a, y_a)$ is known, but not the function $z(x_i,y_i)$
|
||||
because is evaluated in points that are not reflected in the grid, so we must
|
||||
compute this points from the available data. We will start renormalizing the
|
||||
coordinates such that:
|
||||
%
|
||||
\begin{eqnarray}
|
||||
\label{eq:laplace3D:integral:uv}
|
||||
\begin{array}{lcl}
|
||||
u & = & \dsty \frac{x - \left(x_a - Dx\right)}{2 Dx}
|
||||
\\
|
||||
v & = & \dsty \frac{y - \left(y_a - Dy\right)}{2 Dy}
|
||||
\end{array}
|
||||
\end{eqnarray}
|
||||
%
|
||||
So we know the value of $z$ for all the combinations of $u = 0,0.5,1$ and
|
||||
$v = 0,0.5,1$. Then, to can evaluate the function $z(u,v)$ for all $u,v$
|
||||
values we may to build a Spline surface with the data known from the 9
|
||||
points shown in the figure \ref{fig:ss:laplace3D:integral}. The Spline
|
||||
surface can be characterized as
|
||||
%
|
||||
\begin{eqnarray}
|
||||
\label{eq:laplace3D:integral:spline}
|
||||
z(u,v) = k_0 + k_u u + k_v v + k_{uv} u v + k_{uu} u^2 + k_{vv} v^2
|
||||
+ k_{uuv} u^2 v + k_{uvv} u v^2 + k_{uuvv} u^2 v^2
|
||||
\end{eqnarray}
|
||||
%
|
||||
In the equation \ref{eq:laplace3D:integral:spline} we have 9 unknown
|
||||
coefficients, but we have available $z(u,v)$ for 9 points, so have 9
|
||||
unknowns with 9 equations that can be set as a linear system of
|
||||
equations, that results in the following coefficients:
|
||||
%
|
||||
\begin{eqnarray}
|
||||
\label{eq:laplace3D:integral:k}
|
||||
\begin{array}{lcl}
|
||||
k_0 & = & z \left( 0,0 \right)
|
||||
\\
|
||||
k_u & = & - z \left( 1,0 \right) + 4 z \left( \frac{1}{2},0 \right) - 3 z \left( 0,0 \right)
|
||||
\\
|
||||
k_v & = & - z \left( 0,1 \right) + 4 z \left( 0,\frac{1}{2} \right) - 3 z \left( 0,0 \right)
|
||||
\\
|
||||
k_{uv} & = & z \left( 1,1 \right) - 4 z \left( 1,\frac{1}{2} \right) + 3 z \left( 1,0 \right)
|
||||
- 4 z \left( \frac{1}{2},1 \right) + 16 z \left( \frac{1}{2},\frac{1}{2} \right)
|
||||
\\ & &
|
||||
- 12 z \left( \frac{1}{2},0 \right) + 3 z \left( 0,1 \right)
|
||||
- 12 z \left( 0,\frac{1}{2} \right) + 9 z \left( 0,0 \right)
|
||||
\\
|
||||
k_{uu} & = & 2 z \left( 1,0 \right) - 4 z \left( \frac{1}{2},0 \right) + 2 z \left( 1,0 \right)
|
||||
\\
|
||||
k_{vv} & = & 2 z \left( 0,1 \right) - 4 z \left( 0,\frac{1}{2} \right) + 2 z \left( 1,0 \right)
|
||||
\\
|
||||
k_{uuv} & = & - 2 z \left( 1,1 \right) + 8 z \left( 1,\frac{1}{2} \right) - 6 z \left( 1,0 \right)
|
||||
+ 4 z \left( \frac{1}{2},1 \right) - 16 z \left( \frac{1}{2},\frac{1}{2} \right)
|
||||
\\ & &
|
||||
+ 12 z \left( \frac{1}{2},0 \right) - 2 z \left( 0,1 \right)
|
||||
+ 8 z \left( 0,\frac{1}{2} \right) - 6 z \left( 0,0 \right)
|
||||
\\
|
||||
k_{uvv} & = & - 2 z \left( 1,1 \right) + 4 z \left( 1,\frac{1}{2} \right) - 2 z \left( 1,0 \right)
|
||||
+ 8 z \left( \frac{1}{2},1 \right) - 16 z \left( \frac{1}{2},\frac{1}{2} \right)
|
||||
\\ & &
|
||||
+ 8 z \left( \frac{1}{2},0 \right) - 6 z \left( 0,1 \right)
|
||||
+ 12 z \left( 0,\frac{1}{2} \right) - 6 z \left( 0,0 \right)
|
||||
\\
|
||||
k_{uuvv} & = & 4 z \left( 1,1 \right) - 8 z \left( 1,\frac{1}{2} \right) + 4 z \left( 1,0 \right)
|
||||
- 8 z \left( \frac{1}{2},1 \right) + 16 z \left( \frac{1}{2},\frac{1}{2} \right)
|
||||
\\ & &
|
||||
- 8 z \left( \frac{1}{2},0 \right) + 4 z \left( 0,1 \right)
|
||||
- 8 z \left( 0,\frac{1}{2} \right) + 4 z \left( 0,0 \right)
|
||||
\end{array}
|
||||
\end{eqnarray}
|
||||
%
|
||||
So using the equation \ref{eq:laplace3D:integral:g} to \ref{eq:laplace3D:integral:k}
|
||||
we can compute the integrals in the equations \ref{eq:laplace3D:g:hat} and
|
||||
\ref{eq:laplace3D:h:hat}.
|
||||
%
|
||||
\begin{figure}[ht!]
|
||||
\centering
|
||||
\includegraphics[width=0.6\textwidth]{Integral}
|
||||
\caption{Integration method scheme}
|
||||
\label{fig:ss:laplace3D:integral}
|
||||
\end{figure}
|
||||
%
|
||||
\section{BEM test}
|
||||
\label{ss:laplace3D:test}
|
||||
%
|
||||
\subsection{General}
|
||||
\label{sss:laplace3D:test:general}
|
||||
%
|
||||
A Python script has been provided with this document in the subfolder \textbf{test}.
|
||||
In the script all this theory is tested in order to know if the BEM is well purposed,
|
||||
and the errors that can be expected from the method application.\rc
|
||||
%
|
||||
In the test, for the moment, only one wave will be set, and the computational free
|
||||
surface will be big enough to contain 2 wave lengths. In this case a wave period
|
||||
of $T = 2.5 s$ is used, resulting in a wave of 10 meters.\rc
|
||||
%
|
||||
In the figure \ref{fig:laplace3D:test:wave} the wave used, that runs in the x direction,
|
||||
is shown. The free surface will be extended while $G(x,y,z,X,Y,Z) > 0.1$.
|
||||
%
|
||||
\begin{figure}[ht!]
|
||||
\centering
|
||||
\includegraphics[width=0.6\textwidth]{test_wave}
|
||||
\caption{Wave used in the test}
|
||||
\label{fig:laplace3D:test:wave}
|
||||
\end{figure}
|
||||
%
|
||||
\subsection{Direct method}
|
||||
\label{sss:laplace3D:test:direct}
|
||||
%
|
||||
The direct method consist in evaluate the velocity potential in several points
|
||||
using the equation \ref{eq:laplace3D:reciprocal_relation:005}, testing the error
|
||||
get.\rc
|
||||
%
|
||||
If we apply the direct method for all the points of the computational free surface,
|
||||
we can compute the root mean square error as
|
||||
%
|
||||
\begin{eqnarray*}
|
||||
RMS(nx,ny) = \sqrt{\frac{1}{nx \, ny} \sum_{i=1}^{nx} \sum_{j=1}^{ny}
|
||||
\left( \phi_{direct}(x_i,y_j) - \phi(x_i,y_j) \right)^2
|
||||
}
|
||||
\end{eqnarray*}
|
||||
%
|
||||
For $nx = 31$ and $ny = 15$ we have $RMS(31,15) = 0.08$. In the figure
|
||||
\ref{fig:laplace3D:test:direct} the analytic velocity potential, and the
|
||||
interpolated using the direct method, for a slice in the middle of the
|
||||
free surface ($y=0$).\rc
|
||||
%
|
||||
The results quality is good, and can be improved increasing the number of
|
||||
points in the computational free surface.
|
||||
%
|
||||
\begin{figure}[ht!]
|
||||
\centering
|
||||
\includegraphics[width=0.6\textwidth]{test_direct}
|
||||
\caption{Direct method}
|
||||
\label{fig:laplace3D:test:direct}
|
||||
\end{figure}
|
||||
%
|
||||
\subsection{BEM}
|
||||
\label{sss:laplace3D:test:bem}
|
||||
%
|
||||
In this case we want to apply the equation \ref{eq:laplace3D:reciprocal_relation:006},
|
||||
where a linear system of equations is purposed in order to compute the gradient of the
|
||||
velocity potential, projected over the normal, for all the points of the grid.
|
||||
%
|
||||
For $nx = 31$ and $ny = 15$ we have $RMS(31,15) = 0.04$. In the figure
|
||||
\ref{fig:laplace3D:test:bem} the analytic velocity potential, and the
|
||||
interpolated using the direct method, for a slice in the middle of the
|
||||
free surface ($y=0$).\rc
|
||||
%
|
||||
The results quality is nice like in the direct method. In order to get enough good
|
||||
results at least 15 points per wave length must be used (like in this application).
|
||||
%
|
||||
\begin{figure}[ht!]
|
||||
\centering
|
||||
\includegraphics[width=0.6\textwidth]{test_bem}
|
||||
\caption{BEM solution}
|
||||
\label{fig:laplace3D:test:bem}
|
||||
\end{figure}
|
||||
%
|
||||
125
src/Mod/Ship/simRun/theory/main.aux
Normal file
125
src/Mod/Ship/simRun/theory/main.aux
Normal file
|
|
@ -0,0 +1,125 @@
|
|||
\relax
|
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|
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|
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|
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|
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|
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
||||
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
||||
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|
||||
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|
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|
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|
||||
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|
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|
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
||||
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|
||||
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|
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
||||
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|
||||
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|
||||
\bibcite{bem_2007}{{1}{2007}{{Ang}}{{}}}
|
||||
\bibcite{vinayan2007}{{2}{2007}{{Vinayan and Kinnas}}{{}}}
|
||||
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|
||||
\@writefile{toc}{\contentsline {chapter}{Bibliography}{23}{chapter*.2}}
|
||||
24
src/Mod/Ship/simRun/theory/main.bbl
Normal file
24
src/Mod/Ship/simRun/theory/main.bbl
Normal file
|
|
@ -0,0 +1,24 @@
|
|||
\begin{thebibliography}{3}
|
||||
\providecommand{\natexlab}[1]{#1}
|
||||
\providecommand{\url}[1]{\texttt{#1}}
|
||||
\expandafter\ifx\csname urlstyle\endcsname\relax
|
||||
\providecommand{\doi}[1]{doi: #1}\else
|
||||
\providecommand{\doi}{doi: \begingroup \urlstyle{rm}\Url}\fi
|
||||
|
||||
\bibitem[Ang(2007)]{bem_2007}
|
||||
Whye-Teong Ang.
|
||||
\newblock \emph{A Beginner’s Course in Boundary Element Methods}.
|
||||
\newblock Cambridge University Press, New York, 2007.
|
||||
|
||||
\bibitem[Vinayan and Kinnas(2007)]{vinayan2007}
|
||||
V.~Vinayan and S.~A. Kinnas.
|
||||
\newblock A bem for the propagation of nonlinear planar free-surface waves.
|
||||
\newblock \emph{Electronic Journal of Boundary Elements}, 5:\penalty0 17--40,
|
||||
2007.
|
||||
|
||||
\bibitem[Yang(2004)]{yang2004}
|
||||
Jinghai Yang.
|
||||
\newblock \emph{Time domain, nonlinear theories on ship motions}.
|
||||
\newblock PhD thesis, University of Hawaii, 2004.
|
||||
|
||||
\end{thebibliography}
|
||||
48
src/Mod/Ship/simRun/theory/main.blg
Normal file
48
src/Mod/Ship/simRun/theory/main.blg
Normal file
|
|
@ -0,0 +1,48 @@
|
|||
This is BibTeX, Version 0.99d (TeX Live 2012/Debian)
|
||||
Capacity: max_strings=35307, hash_size=35307, hash_prime=30011
|
||||
The top-level auxiliary file: main.aux
|
||||
The style file: plainnat.bst
|
||||
Database file #1: bib.bib
|
||||
Warning--can't use both author and editor fields in bem_2007
|
||||
You've used 3 entries,
|
||||
2773 wiz_defined-function locations,
|
||||
726 strings with 6674 characters,
|
||||
and the built_in function-call counts, 1030 in all, are:
|
||||
= -- 88
|
||||
> -- 41
|
||||
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|
||||
+ -- 15
|
||||
- -- 12
|
||||
* -- 67
|
||||
:= -- 173
|
||||
add.period$ -- 9
|
||||
call.type$ -- 3
|
||||
change.case$ -- 11
|
||||
chr.to.int$ -- 3
|
||||
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|
||||
duplicate$ -- 56
|
||||
empty$ -- 92
|
||||
format.name$ -- 17
|
||||
if$ -- 207
|
||||
int.to.chr$ -- 1
|
||||
int.to.str$ -- 1
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|
||||
(There was 1 warning)
|
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src/Mod/Ship/simRun/theory/main.log
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|
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|
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|
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|
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|
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
defining Unicode char U+2013 (decimal 8211)
|
||||
defining Unicode char U+2014 (decimal 8212)
|
||||
defining Unicode char U+2018 (decimal 8216)
|
||||
defining Unicode char U+2019 (decimal 8217)
|
||||
defining Unicode char U+201A (decimal 8218)
|
||||
defining Unicode char U+201C (decimal 8220)
|
||||
defining Unicode char U+201D (decimal 8221)
|
||||
defining Unicode char U+201E (decimal 8222)
|
||||
defining Unicode char U+2030 (decimal 8240)
|
||||
defining Unicode char U+2031 (decimal 8241)
|
||||
defining Unicode char U+2039 (decimal 8249)
|
||||
defining Unicode char U+203A (decimal 8250)
|
||||
defining Unicode char U+2423 (decimal 9251)
|
||||
)
|
||||
Now handling font encoding OT1 ...
|
||||
... processing UTF-8 mapping file for font encoding OT1
|
||||
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/base/ot1enc.dfu
|
||||
File: ot1enc.dfu 2008/04/05 v1.1m UTF-8 support for inputenc
|
||||
defining Unicode char U+00A1 (decimal 161)
|
||||
defining Unicode char U+00A3 (decimal 163)
|
||||
defining Unicode char U+00B8 (decimal 184)
|
||||
defining Unicode char U+00BF (decimal 191)
|
||||
defining Unicode char U+00C5 (decimal 197)
|
||||
defining Unicode char U+00C6 (decimal 198)
|
||||
defining Unicode char U+00D8 (decimal 216)
|
||||
defining Unicode char U+00DF (decimal 223)
|
||||
defining Unicode char U+00E6 (decimal 230)
|
||||
defining Unicode char U+00EC (decimal 236)
|
||||
defining Unicode char U+00ED (decimal 237)
|
||||
defining Unicode char U+00EE (decimal 238)
|
||||
defining Unicode char U+00EF (decimal 239)
|
||||
defining Unicode char U+00F8 (decimal 248)
|
||||
defining Unicode char U+0131 (decimal 305)
|
||||
defining Unicode char U+0141 (decimal 321)
|
||||
defining Unicode char U+0142 (decimal 322)
|
||||
defining Unicode char U+0152 (decimal 338)
|
||||
defining Unicode char U+0153 (decimal 339)
|
||||
defining Unicode char U+2013 (decimal 8211)
|
||||
defining Unicode char U+2014 (decimal 8212)
|
||||
defining Unicode char U+2018 (decimal 8216)
|
||||
defining Unicode char U+2019 (decimal 8217)
|
||||
defining Unicode char U+201C (decimal 8220)
|
||||
defining Unicode char U+201D (decimal 8221)
|
||||
)
|
||||
Now handling font encoding OMS ...
|
||||
... processing UTF-8 mapping file for font encoding OMS
|
||||
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/base/omsenc.dfu
|
||||
File: omsenc.dfu 2008/04/05 v1.1m UTF-8 support for inputenc
|
||||
defining Unicode char U+00A7 (decimal 167)
|
||||
defining Unicode char U+00B6 (decimal 182)
|
||||
defining Unicode char U+00B7 (decimal 183)
|
||||
defining Unicode char U+2020 (decimal 8224)
|
||||
defining Unicode char U+2021 (decimal 8225)
|
||||
defining Unicode char U+2022 (decimal 8226)
|
||||
)
|
||||
Now handling font encoding OMX ...
|
||||
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|
||||
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|
||||
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|
||||
Now handling font encoding PD1 ...
|
||||
... no UTF-8 mapping file for font encoding PD1
|
||||
defining Unicode char U+00A9 (decimal 169)
|
||||
defining Unicode char U+00AA (decimal 170)
|
||||
defining Unicode char U+00AE (decimal 174)
|
||||
defining Unicode char U+00BA (decimal 186)
|
||||
defining Unicode char U+02C6 (decimal 710)
|
||||
defining Unicode char U+02DC (decimal 732)
|
||||
defining Unicode char U+200C (decimal 8204)
|
||||
defining Unicode char U+2026 (decimal 8230)
|
||||
defining Unicode char U+2122 (decimal 8482)
|
||||
defining Unicode char U+2423 (decimal 9251)
|
||||
))
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/base/alltt.sty
|
||||
Package: alltt 1997/06/16 v2.0g defines alltt environment
|
||||
)
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsmath.sty
|
||||
Package: amsmath 2000/07/18 v2.13 AMS math features
|
||||
\@mathmargin=\skip49
|
||||
|
||||
For additional information on amsmath, use the `?' option.
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amstext.sty
|
||||
Package: amstext 2000/06/29 v2.01
|
||||
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsgen.sty
|
||||
File: amsgen.sty 1999/11/30 v2.0
|
||||
\@emptytoks=\toks21
|
||||
\ex@=\dimen110
|
||||
))
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsbsy.sty
|
||||
Package: amsbsy 1999/11/29 v1.2d
|
||||
\pmbraise@=\dimen111
|
||||
)
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsopn.sty
|
||||
Package: amsopn 1999/12/14 v2.01 operator names
|
||||
)
|
||||
\inf@bad=\count100
|
||||
LaTeX Info: Redefining \frac on input line 211.
|
||||
\uproot@=\count101
|
||||
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|
||||
LaTeX Info: Redefining \overline on input line 307.
|
||||
\classnum@=\count103
|
||||
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|
||||
LaTeX Info: Redefining \ldots on input line 379.
|
||||
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|
||||
LaTeX Info: Redefining \cdots on input line 467.
|
||||
\Mathstrutbox@=\box26
|
||||
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|
||||
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|
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LaTeX Font Info: Redeclaring font encoding OML on input line 567.
|
||||
LaTeX Font Info: Redeclaring font encoding OMS on input line 568.
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
\tag@help=\toks22
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
\lineht@=\dimen118
|
||||
\@envbody=\toks24
|
||||
\multlinegap=\skip50
|
||||
\multlinetaggap=\skip51
|
||||
\mathdisplay@stack=\toks25
|
||||
LaTeX Info: Redefining \[ on input line 2666.
|
||||
LaTeX Info: Redefining \] on input line 2667.
|
||||
)
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/amssymb.sty
|
||||
Package: amssymb 2009/06/22 v3.00
|
||||
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/amsfonts.sty
|
||||
Package: amsfonts 2009/06/22 v3.00 Basic AMSFonts support
|
||||
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|
||||
\symAMSb=\mathgroup5
|
||||
LaTeX Font Info: Overwriting math alphabet `\mathfrak' in version `bold'
|
||||
(Font) U/euf/m/n --> U/euf/b/n on input line 96.
|
||||
))
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/txfonts/txfonts.sty
|
||||
Package: txfonts 2008/01/22 v3.2.1
|
||||
LaTeX Font Info: Redeclaring symbol font `operators' on input line 21.
|
||||
LaTeX Font Info: Overwriting symbol font `operators' in version `normal'
|
||||
(Font) OT1/cmr/m/n --> OT1/txr/m/n on input line 21.
|
||||
LaTeX Font Info: Overwriting symbol font `operators' in version `bold'
|
||||
(Font) OT1/cmr/bx/n --> OT1/txr/m/n on input line 21.
|
||||
LaTeX Font Info: Overwriting symbol font `operators' in version `bold'
|
||||
(Font) OT1/txr/m/n --> OT1/txr/bx/n on input line 22.
|
||||
\symitalic=\mathgroup6
|
||||
LaTeX Font Info: Overwriting symbol font `italic' in version `bold'
|
||||
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|
||||
LaTeX Font Info: Redeclaring math alphabet \mathbf on input line 29.
|
||||
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|
||||
(Font) OT1/cmr/bx/n --> OT1/txr/bx/n on input line 29.
|
||||
LaTeX Font Info: Overwriting math alphabet `\mathbf' in version `bold'
|
||||
(Font) OT1/cmr/bx/n --> OT1/txr/bx/n on input line 29.
|
||||
LaTeX Font Info: Redeclaring math alphabet \mathit on input line 30.
|
||||
LaTeX Font Info: Overwriting math alphabet `\mathit' in version `normal'
|
||||
(Font) OT1/cmr/m/it --> OT1/txr/m/it on input line 30.
|
||||
LaTeX Font Info: Overwriting math alphabet `\mathit' in version `bold'
|
||||
(Font) OT1/cmr/bx/it --> OT1/txr/m/it on input line 30.
|
||||
LaTeX Font Info: Overwriting math alphabet `\mathit' in version `bold'
|
||||
(Font) OT1/txr/m/it --> OT1/txr/bx/it on input line 31.
|
||||
LaTeX Font Info: Redeclaring math alphabet \mathsf on input line 40.
|
||||
LaTeX Font Info: Overwriting math alphabet `\mathsf' in version `normal'
|
||||
(Font) OT1/cmss/m/n --> OT1/txss/m/n on input line 40.
|
||||
LaTeX Font Info: Overwriting math alphabet `\mathsf' in version `bold'
|
||||
(Font) OT1/cmss/bx/n --> OT1/txss/m/n on input line 40.
|
||||
LaTeX Font Info: Overwriting math alphabet `\mathsf' in version `bold'
|
||||
(Font) OT1/txss/m/n --> OT1/txss/b/n on input line 41.
|
||||
LaTeX Font Info: Redeclaring math alphabet \mathtt on input line 50.
|
||||
LaTeX Font Info: Overwriting math alphabet `\mathtt' in version `normal'
|
||||
(Font) OT1/cmtt/m/n --> OT1/txtt/m/n on input line 50.
|
||||
LaTeX Font Info: Overwriting math alphabet `\mathtt' in version `bold'
|
||||
(Font) OT1/cmtt/m/n --> OT1/txtt/m/n on input line 50.
|
||||
LaTeX Font Info: Overwriting math alphabet `\mathtt' in version `bold'
|
||||
(Font) OT1/txtt/m/n --> OT1/txtt/b/n on input line 51.
|
||||
LaTeX Font Info: Redeclaring symbol font `letters' on input line 58.
|
||||
LaTeX Font Info: Overwriting symbol font `letters' in version `normal'
|
||||
(Font) OML/cmm/m/it --> OML/txmi/m/it on input line 58.
|
||||
LaTeX Font Info: Overwriting symbol font `letters' in version `bold'
|
||||
(Font) OML/cmm/b/it --> OML/txmi/m/it on input line 58.
|
||||
LaTeX Font Info: Overwriting symbol font `letters' in version `bold'
|
||||
(Font) OML/txmi/m/it --> OML/txmi/bx/it on input line 59.
|
||||
\symlettersA=\mathgroup7
|
||||
LaTeX Font Info: Overwriting symbol font `lettersA' in version `bold'
|
||||
(Font) U/txmia/m/it --> U/txmia/bx/it on input line 67.
|
||||
LaTeX Font Info: Redeclaring math alphabet \mathfrak on input line 70.
|
||||
LaTeX Font Info: Redeclaring symbol font `symbols' on input line 77.
|
||||
LaTeX Font Info: Overwriting symbol font `symbols' in version `normal'
|
||||
(Font) OMS/cmsy/m/n --> OMS/txsy/m/n on input line 77.
|
||||
LaTeX Font Info: Overwriting symbol font `symbols' in version `bold'
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||||
(Font) OMS/cmsy/b/n --> OMS/txsy/m/n on input line 77.
|
||||
LaTeX Font Info: Overwriting symbol font `symbols' in version `bold'
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(Font) OMS/txsy/m/n --> OMS/txsy/bx/n on input line 78.
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||||
LaTeX Font Info: Redeclaring symbol font `AMSa' on input line 93.
|
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LaTeX Font Info: Overwriting symbol font `AMSa' in version `normal'
|
||||
(Font) U/msa/m/n --> U/txsya/m/n on input line 93.
|
||||
LaTeX Font Info: Overwriting symbol font `AMSa' in version `bold'
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||||
(Font) U/msa/m/n --> U/txsya/m/n on input line 93.
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LaTeX Font Info: Overwriting symbol font `AMSa' in version `bold'
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LaTeX Font Info: Redeclaring symbol font `AMSb' on input line 102.
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LaTeX Font Info: Overwriting symbol font `AMSb' in version `normal'
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(Font) U/msb/m/n --> U/txsyb/m/n on input line 102.
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||||
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||||
LaTeX Font Info: Overwriting symbol font `AMSb' in version `bold'
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(Font) U/txsyb/m/n --> U/txsyb/bx/n on input line 103.
|
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\symsymbolsC=\mathgroup8
|
||||
LaTeX Font Info: Overwriting symbol font `symbolsC' in version `bold'
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||||
(Font) U/txsyc/m/n --> U/txsyc/bx/n on input line 113.
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LaTeX Font Info: Redeclaring symbol font `largesymbols' on input line 120.
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||||
(Font) OMX/cmex/m/n --> OMX/txex/m/n on input line 120.
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||||
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(Font) OMX/cmex/m/n --> OMX/txex/m/n on input line 120.
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LaTeX Font Info: Overwriting symbol font `largesymbols' in version `bold'
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(Font) OMX/txex/m/n --> OMX/txex/bx/n on input line 121.
|
||||
\symlargesymbolsA=\mathgroup9
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LaTeX Font Info: Overwriting symbol font `largesymbolsA' in version `bold'
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(Font) U/txexa/m/n --> U/txexa/bx/n on input line 129.
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LaTeX Info: Redefining \not on input line 1043.
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)
|
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(/usr/share/texlive/texmf-dist/tex/latex/anysize/anysize.sty
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||||
Package: anysize 1994/08/13 setting margin sizes
|
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|
||||
document style option `anysize' loaded
|
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Michael Salzenberg, Thomas Esser, Dirk Hillbrecht
|
||||
Version 1.0, Aug 13, 1994
|
||||
\@Leftmargin=\dimen119
|
||||
\@Rightmargin=\dimen120
|
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) (/usr/share/texlive/texmf-dist/tex/latex/fancyhdr/fancyhdr.sty
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||||
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||||
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|
||||
\f@ncyO@orf=\skip60
|
||||
) (./main.aux)
|
||||
\openout1 = `main.aux'.
|
||||
|
||||
LaTeX Font Info: Checking defaults for OML/txmi/m/it on input line 58.
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||||
LaTeX Font Info: Try loading font information for OML+txmi on input line 58.
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||||
|
||||
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/txfonts/omltxmi.fd
|
||||
File: omltxmi.fd 2000/12/15 v3.1
|
||||
)
|
||||
LaTeX Font Info: ... okay on input line 58.
|
||||
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||||
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|
||||
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||||
LaTeX Font Info: ... okay on input line 58.
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||||
LaTeX Font Info: Checking defaults for OMS/txsy/m/n on input line 58.
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||||
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|
||||
|
||||
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/txfonts/omstxsy.fd
|
||||
File: omstxsy.fd 2000/12/15 v3.1
|
||||
)
|
||||
LaTeX Font Info: ... okay on input line 58.
|
||||
LaTeX Font Info: Checking defaults for OMX/txex/m/n on input line 58.
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||||
LaTeX Font Info: Try loading font information for OMX+txex on input line 58.
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|
||||
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/txfonts/omxtxex.fd
|
||||
File: omxtxex.fd 2000/12/15 v3.1
|
||||
)
|
||||
LaTeX Font Info: ... okay on input line 58.
|
||||
LaTeX Font Info: Checking defaults for U/txexa/m/n on input line 58.
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||||
LaTeX Font Info: Try loading font information for U+txexa on input line 58.
|
||||
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/txfonts/utxexa.fd
|
||||
File: utxexa.fd 2000/12/15 v3.1
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||||
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|
||||
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|
||||
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||||
LaTeX Font Info: ... okay on input line 58.
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||||
LaTeX Font Info: Try loading font information for OT1+txr on input line 58.
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||||
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/txfonts/ot1txr.fd
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||||
File: ot1txr.fd 2000/12/15 v3.1
|
||||
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|
||||
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|
||||
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|
||||
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|
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) (/usr/share/texlive/texmf-dist/tex/latex/oberdiek/epstopdf-base.sty
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||||
Package: epstopdf-base 2010/02/09 v2.5 Base part for package epstopdf
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||||
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|
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|
||||
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|
||||
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|
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|
||||
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|
||||
\AtBeginShipoutBox=\box29
|
||||
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||||
|
||||
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|
||||
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|
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|
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
LaTeX Info: Redefining \ref on input line 58.
|
||||
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|
||||
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||||
|
||||
(./main.out) (./main.out)
|
||||
\@outlinefile=\write3
|
||||
\openout3 = `main.out'.
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||||
|
||||
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|
||||
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/txfonts/utxsya.fd
|
||||
File: utxsya.fd 2000/12/15 v3.1
|
||||
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|
||||
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|
||||
|
||||
(/usr/share/texlive/texmf-dist/tex/latex/txfonts/utxsyb.fd
|
||||
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|
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|
||||
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src/Mod/Ship/simRun/theory/main.out
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|||
\BOOKMARK [0][-]{chapter.1}{Introduction}{}% 1
|
||||
\BOOKMARK [1][-]{section.1.1}{Objective}{chapter.1}% 2
|
||||
\BOOKMARK [0][-]{chapter.2}{Governing equations}{}% 3
|
||||
\BOOKMARK [0][-]{chapter.3}{Waves propagations in 2D plane}{}% 4
|
||||
\BOOKMARK [1][-]{section.3.1}{General}{chapter.3}% 5
|
||||
\BOOKMARK [1][-]{section.3.2}{Incident waves}{chapter.3}% 6
|
||||
\BOOKMARK [1][-]{section.3.3}{BEM applied to Laplace 2D problem}{chapter.3}% 7
|
||||
\BOOKMARK [1][-]{section.3.4}{Conclusions to Laplace 2D problem}{chapter.3}% 8
|
||||
\BOOKMARK [0][-]{chapter.4}{Waves propagations in 3D}{}% 9
|
||||
\BOOKMARK [1][-]{section.4.1}{General}{chapter.4}% 10
|
||||
\BOOKMARK [1][-]{section.4.2}{Incident waves}{chapter.4}% 11
|
||||
\BOOKMARK [1][-]{section.4.3}{BEM applied to Laplace 3D problem}{chapter.4}% 12
|
||||
\BOOKMARK [2][-]{subsection.4.3.1}{Computational domain}{section.4.3}% 13
|
||||
\BOOKMARK [2][-]{subsection.4.3.2}{Boundary conditions \(BC\)}{section.4.3}% 14
|
||||
\BOOKMARK [2][-]{subsection.4.3.3}{Time integration scheme}{section.4.3}% 15
|
||||
\BOOKMARK [2][-]{subsection.4.3.4}{Discrete Laplace solution using the BEM}{section.4.3}% 16
|
||||
\BOOKMARK [2][-]{subsection.4.3.5}{Integrals computation}{section.4.3}% 17
|
||||
\BOOKMARK [1][-]{section.4.4}{BEM test}{chapter.4}% 18
|
||||
\BOOKMARK [2][-]{subsection.4.4.1}{General}{section.4.4}% 19
|
||||
\BOOKMARK [2][-]{subsection.4.4.2}{Direct method}{section.4.4}% 20
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\BOOKMARK [2][-]{subsection.4.4.3}{BEM}{section.4.4}% 21
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\BOOKMARK [0][-]{chapter*.2}{Bibliography}{}% 22
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\documentclass[a4paper,12pt]{book}
|
||||
\usepackage[numbers]{natbib}
|
||||
\bibliographystyle{plainnat}
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||||
\usepackage{graphicx}
|
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\usepackage{verbatim}
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\usepackage{color, colortbl}
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\usepackage{hyperref}
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\usepackage[utf8]{inputenc}
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\setcounter{tocdepth}{2}
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\usepackage{alltt}
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\usepackage{amsmath}
|
||||
\usepackage{amssymb}
|
||||
\usepackage{amsfonts}
|
||||
\graphicspath{{./images/}}
|
||||
\usepackage{txfonts} %%does not work on Windows
|
||||
% \usepackage{dsfont}
|
||||
%
|
||||
\newcommand{\NAME}{FreeCAD-Ship }
|
||||
\newcommand{\rc}{\\[0.2 in]}
|
||||
\newcommand{\rcc}{\\[0.3 in]}
|
||||
\newcommand{\rccc}{\\[0.4 in]}
|
||||
% \newcommand{\bs}[1]{\boldsymbol{#1}}
|
||||
\newcommand{\bs}[1]{\pmb{#1}}
|
||||
\newcommand{\SPHint}{\int_{\bs{y} \in \Omega}}
|
||||
\newcommand{\SPHboundint}{\int_{\bs{y} \in \partial \Omega}}
|
||||
\newcommand{\gradient}{\nabla}
|
||||
\newcommand{\divergence}{\mbox{div}}
|
||||
\newcommand{\rotational}{\nabla \times}
|
||||
\newcommand{\laplacian}{\bigtriangleup}
|
||||
\newcommand{\dsty}{\displaystyle}
|
||||
\newcommand{\sph}[1]{\langle {#1} \rangle}
|
||||
%
|
||||
\author{JL Cercos-Pita $<$jlcercos@gmail.com$>$}
|
||||
\title{FreeCAD-Ship.\rcc
|
||||
\textbf{Sea waves transport using Boundary Elements Method}}
|
||||
\date{\today\\[5.0 in]
|
||||
\begin{figure}[h!]
|
||||
\centering
|
||||
\includegraphics[width=0.2\textwidth]{CC_88x31}
|
||||
\end{figure}
|
||||
}
|
||||
%
|
||||
\setlength{\parindent}{0em}
|
||||
%
|
||||
\usepackage{anysize}
|
||||
\marginsize{1.5cm}{1cm}{1cm}{1cm}
|
||||
%
|
||||
\usepackage{fancyhdr}
|
||||
\pagestyle{fancyplain}
|
||||
% Pages header and foot
|
||||
\lhead{}
|
||||
\rhead{\NAME}
|
||||
\lfoot{JL Cercos-Pita}
|
||||
\cfoot{jlcercos@gmail.com}
|
||||
\rfoot{\thepage}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\begin{document}
|
||||
|
||||
% -------------------------------
|
||||
% Title and summary
|
||||
% -------------------------------
|
||||
\maketitle
|
||||
\thispagestyle{empty}
|
||||
%
|
||||
\newpage
|
||||
\tableofcontents
|
||||
\newpage
|
||||
\newpage
|
||||
% -------------------------------
|
||||
% Introduction
|
||||
% -------------------------------
|
||||
\input{abstract}
|
||||
|
||||
% -------------------------------
|
||||
% Laplacian 2D
|
||||
% -------------------------------
|
||||
\input{laplace2D}
|
||||
|
||||
% -------------------------------
|
||||
% Laplacian 2D
|
||||
% -------------------------------
|
||||
\input{laplace3D}
|
||||
|
||||
% -------------------------------
|
||||
% Bibliography
|
||||
% -------------------------------
|
||||
\bibliography{bib}
|
||||
\addcontentsline{toc}{chapter}{Bibliography}
|
||||
\end{document}
|
||||
22
src/Mod/Ship/simRun/theory/main.toc
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|
|
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|
|||
\contentsline {chapter}{\numberline {1}Introduction}{5}{chapter.1}
|
||||
\contentsline {section}{\numberline {1.1}Objective}{5}{section.1.1}
|
||||
\contentsline {chapter}{\numberline {2}Governing equations}{7}{chapter.2}
|
||||
\contentsline {chapter}{\numberline {3}Waves propagations in 2D plane}{9}{chapter.3}
|
||||
\contentsline {section}{\numberline {3.1}General}{9}{section.3.1}
|
||||
\contentsline {section}{\numberline {3.2}Incident waves}{9}{section.3.2}
|
||||
\contentsline {section}{\numberline {3.3}BEM applied to Laplace 2D problem}{10}{section.3.3}
|
||||
\contentsline {section}{\numberline {3.4}Conclusions to Laplace 2D problem}{11}{section.3.4}
|
||||
\contentsline {chapter}{\numberline {4}Waves propagations in 3D}{13}{chapter.4}
|
||||
\contentsline {section}{\numberline {4.1}General}{13}{section.4.1}
|
||||
\contentsline {section}{\numberline {4.2}Incident waves}{13}{section.4.2}
|
||||
\contentsline {section}{\numberline {4.3}BEM applied to Laplace 3D problem}{13}{section.4.3}
|
||||
\contentsline {subsection}{\numberline {4.3.1}Computational domain}{13}{subsection.4.3.1}
|
||||
\contentsline {subsection}{\numberline {4.3.2}Boundary conditions (BC)}{14}{subsection.4.3.2}
|
||||
\contentsline {subsection}{\numberline {4.3.3}Time integration scheme}{15}{subsection.4.3.3}
|
||||
\contentsline {subsection}{\numberline {4.3.4}Discrete Laplace solution using the BEM}{16}{subsection.4.3.4}
|
||||
\contentsline {subsection}{\numberline {4.3.5}Integrals computation}{17}{subsection.4.3.5}
|
||||
\contentsline {section}{\numberline {4.4}BEM test}{18}{section.4.4}
|
||||
\contentsline {subsection}{\numberline {4.4.1}General}{18}{subsection.4.4.1}
|
||||
\contentsline {subsection}{\numberline {4.4.2}Direct method}{19}{subsection.4.4.2}
|
||||
\contentsline {subsection}{\numberline {4.4.3}BEM}{20}{subsection.4.4.3}
|
||||
\contentsline {chapter}{Bibliography}{23}{chapter*.2}
|
||||
127
src/Mod/Ship/simRun/theory/test/green.py
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src/Mod/Ship/simRun/theory/test/green.py
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|
|
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|
|||
#***************************************************************************
|
||||
#* *
|
||||
#* Copyright (c) 2011, 2012 *
|
||||
#* Jose Luis Cercos Pita <jlcercos@gmail.com> *
|
||||
#* *
|
||||
#* This program is free software; you can redistribute it and/or modify *
|
||||
#* it under the terms of the GNU Lesser General Public License (LGPL) *
|
||||
#* as published by the Free Software Foundation; either version 2 of *
|
||||
#* the License, or (at your option) any later version. *
|
||||
#* for detail see the LICENCE text file. *
|
||||
#* *
|
||||
#* This program is distributed in the hope that it will be useful, *
|
||||
#* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||
#* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
|
||||
#* GNU Library General Public License for more details. *
|
||||
#* *
|
||||
#* You should have received a copy of the GNU Library General Public *
|
||||
#* License along with this program; if not, write to the Free Software *
|
||||
#* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 *
|
||||
#* USA *
|
||||
#* *
|
||||
#***************************************************************************
|
||||
|
||||
from numpy import *
|
||||
|
||||
import waves
|
||||
|
||||
def G_val(x,X):
|
||||
""" Computed the Green's function value.
|
||||
@param x Point to evaluate (numpy.array(3))
|
||||
@param X Reference point (numpy.array(3))
|
||||
@return Green's function value.
|
||||
"""
|
||||
return 1.0 / (4.0*pi * linalg.norm(x-X))
|
||||
|
||||
def H_val(x,X):
|
||||
""" Computed the Green's function gradient.
|
||||
@param x Point to evaluate (numpy.array(3))
|
||||
@param X Reference point (numpy.array(3))
|
||||
@return Green's function gradient.
|
||||
"""
|
||||
return (x-X) / (4.0*pi * dot(x-X, x-X)**1.5 )
|
||||
|
||||
def GH(p,I,J,P,n,L,B,x,y,z,dx,dy,t, a,k,w,d):
|
||||
""" Computes the Green's function integral
|
||||
numerically, with an increase resolution of n.
|
||||
@param p Point to evaluate
|
||||
@param I Point to evaluate x index
|
||||
@param J Point to evaluate y index
|
||||
@param P Reference point
|
||||
@param n Number of divisors in each direction to
|
||||
discretize each area element. Should be an even value
|
||||
@param L Length of the computational domain
|
||||
@param B width of the computational domain
|
||||
@param x X coordinates of the area elements
|
||||
@param y Y coordinates of the area elements
|
||||
@param z Z coordinates of the area elements
|
||||
@param dx distance between elements in the x direction
|
||||
@param dy distance between elements in the y direction
|
||||
@param t Simulation time (s)
|
||||
@param a List of waves amplitudes
|
||||
@param k List of waves k
|
||||
@param w List of waves omega
|
||||
@param d List of waves lags.
|
||||
@return Green's function integral.
|
||||
"""
|
||||
# Ensure that n is an even value. If n is even
|
||||
# we can grant that any point will be placed
|
||||
# in p, that can be eventually the same than
|
||||
# P, being G and H functions bad defined.
|
||||
if n % 2:
|
||||
n = n + 1
|
||||
# Get the new distance between Green's points
|
||||
DX = dx / n
|
||||
DY = dy / n
|
||||
# Get the coordinates of all the grid points
|
||||
# around the evaluation one
|
||||
nx = x.shape[0]
|
||||
ny = y.shape[1]
|
||||
X = zeros((3,3),dtype=float32)
|
||||
Y = zeros((3,3),dtype=float32)
|
||||
Z = zeros((3,3),dtype=float32)
|
||||
for i in range(0,3):
|
||||
for j in range(0,3):
|
||||
X[i,j] = p[0] + (i-1)*dx
|
||||
Y[i,j] = p[1] + (j-1)*dy
|
||||
if((X[i,j] > -0.5*L) and (X[i,j] < 0.5*L) and (Y[i,j] > -0.5*B) and (Y[i,j] < 0.5*B)):
|
||||
Z[i,j] = z[I-1+i,J-1+j]
|
||||
else:
|
||||
Z[i,j] = waves.z(X[i,j],Y[i,j],t, a,k,w,d)
|
||||
# Perform spline surface coeffs
|
||||
K = zeros((3*3),dtype=float32)
|
||||
K[0] = Z[0,0] # k_{0}
|
||||
K[1] = 4*Z[1,0] - Z[2,0] - 3*Z[0,0] # k_{u}
|
||||
K[2] = 4*Z[0,1] - Z[0,2] - 3*Z[0,0] # k_{v}
|
||||
K[3] = Z[2,2] - 4*Z[2,1] + 3*Z[2,0] + \
|
||||
3*Z[0,2] - 12*Z[0,1] + 9*Z[0,0] + \
|
||||
-4*Z[1,2] + 16*Z[1,1] - 12*Z[1,0] # k_{uv}
|
||||
K[4] = 2*Z[2,0] + 2*Z[0,0] - 4*Z[1,0] # k_{uu}
|
||||
K[5] = 2*Z[0,2] + 2*Z[0,0] - 4*Z[0,1] # k_{vv}
|
||||
K[6] = -2*Z[2,2] + 8*Z[2,1] - 6*Z[2,0] + \
|
||||
-2*Z[0,2] + 8*Z[0,1] - 6*Z[0,0] + \
|
||||
4*Z[1,2] - 16*Z[1,1] + 12*Z[1,0] # k_{uuv}
|
||||
K[7] = -2*Z[2,2] + 4*Z[2,1] - 2*Z[2,0] + \
|
||||
-6*Z[0,2] + 12*Z[0,1] - 6*Z[0,0] + \
|
||||
8*Z[1,2] - 16*Z[1,1] + 8*Z[1,0] # k_{uuv}
|
||||
K[8] = 4*Z[2,2] - 8*Z[2,1] + 4*Z[2,0] + \
|
||||
4*Z[0,2] - 8*Z[0,1] + 4*Z[0,0] + \
|
||||
-8*Z[1,2] + 16*Z[1,1] - 8*Z[1,0] # k_{uuvv}
|
||||
# Loop around the point p collecting the integral
|
||||
G_tot = 0.0
|
||||
H_tot = zeros((3),dtype=float32)
|
||||
for i in range(0,n):
|
||||
for j in range(0,n):
|
||||
xx = x[I,J] - 0.5*dx + (i+0.5)*DX
|
||||
yy = y[I,J] - 0.5*dy + (j+0.5)*DY
|
||||
# Interpolate z
|
||||
u = (xx - X[0,0]) / (X[2,0] - X[0,0])
|
||||
v = (yy - Y[0,0]) / (Y[0,2] - Y[0,0])
|
||||
zz = K[0] + K[1]*u + K[2]*v + K[3]*u*v + \
|
||||
K[4]*u*u + K[5]*v*v + K[6]*u*u*v + \
|
||||
K[7]*u*v*v + K[8]*u*u*v*v
|
||||
p = array([xx,yy,zz])
|
||||
G_tot = G_tot + G_val(p,P)*DX*DY
|
||||
H_tot = H_tot + H_val(p,P)*DX*DY
|
||||
return (G_tot,H_tot)
|
||||
|
||||
285
src/Mod/Ship/simRun/theory/test/main.py
Normal file
285
src/Mod/Ship/simRun/theory/test/main.py
Normal file
|
|
@ -0,0 +1,285 @@
|
|||
#***************************************************************************
|
||||
#* *
|
||||
#* Copyright (c) 2011, 2012 *
|
||||
#* Jose Luis Cercos Pita <jlcercos@gmail.com> *
|
||||
#* *
|
||||
#* This program is free software; you can redistribute it and/or modify *
|
||||
#* it under the terms of the GNU Lesser General Public License (LGPL) *
|
||||
#* as published by the Free Software Foundation; either version 2 of *
|
||||
#* the License, or (at your option) any later version. *
|
||||
#* for detail see the LICENCE text file. *
|
||||
#* *
|
||||
#* This program is distributed in the hope that it will be useful, *
|
||||
#* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||
#* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
|
||||
#* GNU Library General Public License for more details. *
|
||||
#* *
|
||||
#* You should have received a copy of the GNU Library General Public *
|
||||
#* License along with this program; if not, write to the Free Software *
|
||||
#* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 *
|
||||
#* USA *
|
||||
#* *
|
||||
#***************************************************************************
|
||||
|
||||
import sys
|
||||
from numpy import*
|
||||
import scipy.linalg as la
|
||||
from pylab import *
|
||||
|
||||
from green import *
|
||||
import waves
|
||||
|
||||
# ---------------------------------------------------
|
||||
# Input data
|
||||
# ---------------------------------------------------
|
||||
|
||||
# Computational free surface (the part where we will
|
||||
# compute the fluid dynamics) definition
|
||||
L = 20.0
|
||||
B = 10.0
|
||||
nx = 31
|
||||
ny = 15
|
||||
|
||||
# Waves to use, defined by the wave amplitude period,
|
||||
# and lag. X direction waves will be assumed.
|
||||
# l = g*T^2 / (2*pi)
|
||||
a = [0.1]
|
||||
t = [2.5]
|
||||
d = [0.0]
|
||||
|
||||
# Green's function maximum value (Error). Used to compute
|
||||
# The maximum distance to extend the free surface.
|
||||
G_error = 1e-1
|
||||
|
||||
# Green's functions integrals resolution (even values)
|
||||
nG = 8
|
||||
|
||||
# ---------------------------------------------------
|
||||
# Simulation setup
|
||||
# ---------------------------------------------------
|
||||
|
||||
# Discretization
|
||||
drx = L / nx
|
||||
dry = B / ny
|
||||
dS = drx*dry
|
||||
|
||||
# First we may compute how many domains must be
|
||||
# included in each directions to reach the Green's
|
||||
# function requested error.
|
||||
x = (L-drx)/2.0
|
||||
Nx = 0
|
||||
Gx = G_error*10.0
|
||||
while(Gx > G_error):
|
||||
x = x + L
|
||||
Nx = Nx + 1
|
||||
p = zeros((3), dtype=float32)
|
||||
P = zeros((3), dtype=float32)
|
||||
p[0] = x
|
||||
Gx = G_val(p,P)
|
||||
print('{0} times the free surface must be duplicated in the x direction\n\tG={1}'.format(Nx,Gx))
|
||||
|
||||
y = (B-dry)/2.0
|
||||
Ny = 0
|
||||
Gy = G_error*10.0
|
||||
while(Gy > G_error):
|
||||
y = y + B
|
||||
Ny = Ny + 1
|
||||
p = zeros((3), dtype=float32)
|
||||
P = zeros((3), dtype=float32)
|
||||
p[1] = y
|
||||
Gy = G_val(p,P)
|
||||
print('{0} times the free surface must be duplicated in the y direction\n\tG={1}'.format(Ny,Gy))
|
||||
|
||||
# Now we can compute some additional data of the waves
|
||||
k = []
|
||||
w = []
|
||||
c = []
|
||||
for i in range(0,len(a)):
|
||||
w.append(2*pi/t[i])
|
||||
k.append(w[i]**2 / 9.81)
|
||||
c.append(w[i]/k[i])
|
||||
|
||||
# We can intializate the free surface
|
||||
x = zeros((nx,ny),dtype=float32)
|
||||
y = zeros((nx,ny),dtype=float32)
|
||||
z = zeros((nx,ny),dtype=float32)
|
||||
gradz = zeros((nx,ny),dtype=float32)
|
||||
p = zeros((nx,ny),dtype=float32)
|
||||
gradp = zeros((nx,ny),dtype=float32)
|
||||
for i in range(0,nx):
|
||||
for j in range(0,ny):
|
||||
x[i,j] = -0.5*L + (i+0.5)*drx
|
||||
y[i,j] = -0.5*B + (j+0.5)*dry
|
||||
z[i,j] = waves.z(x[i,j],y[i,j],0.0, a,k,w,d)
|
||||
p[i,j] = waves.phi(x[i,j],y[i,j],z[i,j],0.0, a,k,w,d)
|
||||
gradp[i,j] = waves.gradphi(x[i,j],y[i,j],z[i,j],0.0, a,k,w,d)[2]
|
||||
|
||||
# We can plot starting data
|
||||
plot_j = int(ny/2)
|
||||
fig = figure()
|
||||
plot(x[:,plot_j], z[:,plot_j], color="blue", linewidth=2.5, linestyle="-", label="z")
|
||||
plot(x[:,plot_j], gradp[:,plot_j], color="red", linewidth=2.5, linestyle="-", label="vz")
|
||||
plot(x[:,plot_j], p[:,plot_j], color="green", linewidth=2.5, linestyle="-", label="phi")
|
||||
legend(loc='best')
|
||||
grid()
|
||||
show()
|
||||
close(fig)
|
||||
|
||||
# Compute the error in an arbitrary point
|
||||
phi = zeros((nx,ny),dtype=float32)
|
||||
i = int(nx/2)
|
||||
j = int(ny/2)
|
||||
xx = x[i,j]
|
||||
yy = y[i,j]
|
||||
zz = z[i,j]
|
||||
pp = array([xx,yy,zz])
|
||||
print('Testing direct method in the point ({0}, {1}, {2})'.format(pp[0],pp[1],pp[2]))
|
||||
for I in range(0,nx):
|
||||
for J in range(0,ny):
|
||||
# Get phi from this point
|
||||
XX = x[I,J]
|
||||
YY = y[I,J]
|
||||
ZZ = z[I,J]
|
||||
PP = array([XX,YY,ZZ])
|
||||
if((I,J) == (i,j)):
|
||||
# if (I in range(i-1,i+2)) or (J in range(j-1,j+2)):
|
||||
G,H = GH(PP,I,J,pp,nG,L,B,x,y,z,drx,dry,0.0, a,k,w,d)
|
||||
else:
|
||||
G = G_val(PP,pp)*dS
|
||||
H = H_val(PP,pp)*dS
|
||||
phi[i,j] = phi[i,j] - (p[I,J]*H[2] - gradp[I,J]*G)
|
||||
# Get phi from the extended free surface
|
||||
for II in range(-Nx,Nx+1):
|
||||
for JJ in range(-Ny,Ny+1):
|
||||
if (not II) and (not JJ):
|
||||
# This is the computational domain
|
||||
continue
|
||||
XX = x[I,J] + II*L
|
||||
YY = y[I,J] + JJ*B
|
||||
ZZ = waves.z(XX,YY,0.0, a,k,w,d)
|
||||
PP = array([XX,YY,ZZ])
|
||||
Phi = waves.phi(XX,YY,ZZ,0.0, a,k,w,d)
|
||||
gPhi = waves.gradphi(XX,YY,ZZ,0.0, a,k,w,d)[2]
|
||||
phi[i,j] = phi[i,j] - (Phi*H_val(PP,pp)[2] - gPhi*G_val(PP,pp))*dS
|
||||
# Correct phi
|
||||
phi[i,j] = 2.0*phi[i,j]
|
||||
print('Computed = {0}, analitic = {1}\n'.format(phi[i,j],p[i,j]))
|
||||
|
||||
# Compute the error along all the free surface
|
||||
phi = zeros((nx,ny),dtype=float32)
|
||||
error = 0.0
|
||||
done = 0
|
||||
print('Testing direct method in all the free surface')
|
||||
for i in range(0,nx):
|
||||
for j in range(0,ny):
|
||||
if done != (100*(j + i*ny))/(nx*ny):
|
||||
done = (100*(j + i*ny))/(nx*ny)
|
||||
sys.stdout.write("{0}%...".format(done))
|
||||
sys.stdout.flush()
|
||||
xx = x[i,j]
|
||||
yy = y[i,j]
|
||||
zz = z[i,j]
|
||||
pp = array([xx,yy,zz])
|
||||
for I in range(0,nx):
|
||||
for J in range(0,ny):
|
||||
# Get phi from this point
|
||||
XX = x[I,J]
|
||||
YY = y[I,J]
|
||||
ZZ = z[I,J]
|
||||
PP = array([XX,YY,ZZ])
|
||||
if((I,J) == (i,j)):
|
||||
# if (I in range(i-1,i+2)) or (J in range(j-1,j+2)):
|
||||
G,H = GH(PP,I,J,pp,nG,L,B,x,y,z,drx,dry,0.0, a,k,w,d)
|
||||
else:
|
||||
G = G_val(PP,pp)*dS
|
||||
H = H_val(PP,pp)*dS
|
||||
phi[i,j] = phi[i,j] - (p[I,J]*H[2] - gradp[I,J]*G)
|
||||
# Get phi from the extended free surface
|
||||
for II in range(-Nx,Nx+1):
|
||||
for JJ in range(-Ny,Ny+1):
|
||||
if (not II) and (not JJ):
|
||||
# This is the computational domain
|
||||
continue
|
||||
XX = x[I,J] + II*L
|
||||
YY = y[I,J] + JJ*B
|
||||
ZZ = waves.z(XX,YY,0.0, a,k,w,d)
|
||||
PP = array([XX,YY,ZZ])
|
||||
Phi = waves.phi(XX,YY,ZZ,0.0, a,k,w,d)
|
||||
gPhi = waves.gradphi(XX,YY,ZZ,0.0, a,k,w,d)[2]
|
||||
phi[i,j] = phi[i,j] - (Phi*H_val(PP,pp)[2] - gPhi*G_val(PP,pp))*dS
|
||||
# Correct phi
|
||||
phi[i,j] = 2.0*phi[i,j]
|
||||
error = error + (phi[i,j] - p[i,j])**2
|
||||
error = sqrt(error / (nx*ny))
|
||||
print('\nRoot mean square error = {0}\n'.format(error))
|
||||
fig = figure()
|
||||
plot(x[:,plot_j], p[:,plot_j], color="blue", linewidth=2.5, linestyle="-", label="analitic")
|
||||
plot(x[:,plot_j], phi[:,plot_j], color="red", linewidth=2.5, linestyle="-", label="interpolated")
|
||||
legend(loc='best')
|
||||
grid()
|
||||
show()
|
||||
close(fig)
|
||||
|
||||
# Compute the BEM
|
||||
GG = zeros((nx*ny, nx*ny), dtype=float32)
|
||||
HH = -0.5 * array(identity(nx*ny),dtype=float32)
|
||||
BB = zeros((nx*ny), dtype=float32)
|
||||
error = 0.0
|
||||
done = 0
|
||||
print('Testing BEM in all the free surface')
|
||||
for i in range(0,nx):
|
||||
for j in range(0,ny):
|
||||
if done != (100*(j + i*ny))/(nx*ny):
|
||||
done = (100*(j + i*ny))/(nx*ny)
|
||||
sys.stdout.write("{0}%...".format(done))
|
||||
sys.stdout.flush()
|
||||
xx = x[i,j]
|
||||
yy = y[i,j]
|
||||
zz = z[i,j]
|
||||
pp = array([xx,yy,zz])
|
||||
for I in range(0,nx):
|
||||
for J in range(0,ny):
|
||||
# Get phi from this point
|
||||
XX = x[I,J]
|
||||
YY = y[I,J]
|
||||
ZZ = z[I,J]
|
||||
PP = array([XX,YY,ZZ])
|
||||
if((I,J) == (i,j)):
|
||||
# if (I in range(i-1,i+2)) or (J in range(j-1,j+2)):
|
||||
G,H = GH(PP,I,J,pp,nG,L,B,x,y,z,drx,dry,0.0, a,k,w,d)
|
||||
else:
|
||||
G = G_val(PP,pp)*dS
|
||||
H = H_val(PP,pp)*dS
|
||||
GG[j + i*ny,J + I*ny] = GG[j + i*ny,J + I*ny] - G
|
||||
HH[j + i*ny,J + I*ny] = HH[j + i*ny,J + I*ny] - H[2]
|
||||
# Get phi from the extended free surface
|
||||
for II in range(-Nx,Nx+1):
|
||||
for JJ in range(-Ny,Ny+1):
|
||||
if (not II) and (not JJ):
|
||||
# This is the computational domain
|
||||
continue
|
||||
XX = x[I,J] + II*L
|
||||
YY = y[I,J] + JJ*B
|
||||
ZZ = waves.z(XX,YY,0.0, a,k,w,d)
|
||||
PP = array([XX,YY,ZZ])
|
||||
Phi = waves.phi(XX,YY,ZZ,0.0, a,k,w,d)
|
||||
gPhi = waves.gradphi(XX,YY,ZZ,0.0, a,k,w,d)[2]
|
||||
BB[j + i*ny] = BB[j + i*ny] - (Phi*H_val(PP,pp)[2] - gPhi*G_val(PP,pp))*dS
|
||||
[gPhi, residues, rank, s] = la.lstsq(GG, dot(HH,p.reshape(nx*ny)) + BB)
|
||||
gPhi = gPhi.reshape(nx,ny)
|
||||
if(rank < nx*ny):
|
||||
print("Singular matrix G!.\n")
|
||||
print("\tEffective rank of linear system matrix is %i (N = %i)\n" % (rank, nx*ny))
|
||||
for i in range(0,nx):
|
||||
for j in range(0,ny):
|
||||
error = error + (gPhi[i,j] - gradp[i,j])**2
|
||||
error = sqrt(error / (nx*ny))
|
||||
print('\nRoot mean square error = {0}\n'.format(error))
|
||||
fig = figure()
|
||||
plot(x[:,plot_j], gradp[:,plot_j], color="blue", linewidth=2.5, linestyle="-", label="analitic")
|
||||
plot(x[:,plot_j], gPhi[:,plot_j], color="red", linewidth=2.5, linestyle="-", label="interpolated")
|
||||
legend(loc='best')
|
||||
grid()
|
||||
show()
|
||||
close(fig)
|
||||
|
||||
94
src/Mod/Ship/simRun/theory/test/waves.py
Normal file
94
src/Mod/Ship/simRun/theory/test/waves.py
Normal file
|
|
@ -0,0 +1,94 @@
|
|||
#***************************************************************************
|
||||
#* *
|
||||
#* Copyright (c) 2011, 2012 *
|
||||
#* Jose Luis Cercos Pita <jlcercos@gmail.com> *
|
||||
#* *
|
||||
#* This program is free software; you can redistribute it and/or modify *
|
||||
#* it under the terms of the GNU Lesser General Public License (LGPL) *
|
||||
#* as published by the Free Software Foundation; either version 2 of *
|
||||
#* the License, or (at your option) any later version. *
|
||||
#* for detail see the LICENCE text file. *
|
||||
#* *
|
||||
#* This program is distributed in the hope that it will be useful, *
|
||||
#* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||
#* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
|
||||
#* GNU Library General Public License for more details. *
|
||||
#* *
|
||||
#* You should have received a copy of the GNU Library General Public *
|
||||
#* License along with this program; if not, write to the Free Software *
|
||||
#* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 *
|
||||
#* USA *
|
||||
#* *
|
||||
#***************************************************************************
|
||||
|
||||
from numpy import *
|
||||
from green import *
|
||||
|
||||
def z(x,y,t, a,k,w,d):
|
||||
""" Returns free surface shape
|
||||
@param x X coordinate
|
||||
@param y Y coordinate
|
||||
@param t Time instant
|
||||
@param a List of waves amplitudes
|
||||
@param k List of waves k
|
||||
@param w List of waves omega
|
||||
@param d List of waves lags.
|
||||
@return free surface elevation
|
||||
"""
|
||||
Z = 0.0
|
||||
for i in range(0,len(a)):
|
||||
Z = Z + a[i]*sin(k[i]*x - w[i]*t + d[i])
|
||||
return Z
|
||||
|
||||
def gradz(x,y,t, a,k,w,d):
|
||||
""" Returns free surface shape gradient
|
||||
@param x X coordinate
|
||||
@param y Y coordinate
|
||||
@param t Time instant
|
||||
@param a List of waves amplitudes
|
||||
@param k List of waves k
|
||||
@param w List of waves omega
|
||||
@param d List of waves lags.
|
||||
@return free surface elevation
|
||||
"""
|
||||
gradZ = zeros((3), dtype=float32)
|
||||
gradZ[2] = 1.0
|
||||
for i in range(0,len(a)):
|
||||
gradZ[0] = gradZ[0] + a[i]*k[i]*cos(k[i]*x - w[i]*t + d[i])
|
||||
return gradZ
|
||||
|
||||
def phi(x,y,z,t, a,k,w,d):
|
||||
""" Returns velocity potential
|
||||
@param x X coordinate
|
||||
@param y Y coordinate
|
||||
@param z Free surface elevation
|
||||
@param t Time instant
|
||||
@param a List of waves amplitudes
|
||||
@param k List of waves k
|
||||
@param w List of waves omega
|
||||
@param d List of waves lags.
|
||||
@return Velocity potential
|
||||
"""
|
||||
p = 0.0
|
||||
for i in range(0,len(a)):
|
||||
p = p - a[i]*w[i]/k[i]*cos(k[i]*x - w[i]*t + d[i])*exp(k[i]*z)
|
||||
return p
|
||||
|
||||
def gradphi(x,y,z,t, a,k,w,d):
|
||||
""" Returns velocity potential gradient
|
||||
@param x X coordinate
|
||||
@param y Y coordinate
|
||||
@param z Free surface elevation
|
||||
@param t Time instant
|
||||
@param a List of waves amplitudes
|
||||
@param k List of waves k
|
||||
@param w List of waves omega
|
||||
@param d List of waves lags.
|
||||
@return velocity potential gradient
|
||||
"""
|
||||
gradp = zeros((3), dtype=float32)
|
||||
for i in range(0,len(a)):
|
||||
gradp[0] = gradp[0] + a[i]*w[i]*sin(k[i]*x - w[i]*t + d[i])*exp(k[i]*z)
|
||||
gradp[2] = gradp[2] - a[i]*w[i]*cos(k[i]*x - w[i]*t + d[i])*exp(k[i]*z)
|
||||
return gradp
|
||||
|
||||
Loading…
Reference in New Issue
Block a user