def main(path='./'):
if len(sys.argv) == 2:
path = sys.argv[1]
interpOrders = [1, 2, 3, 4]
gl = gridlayout.GridLayout()
directions = gl.directions
quantities = gl.hybridQuantities
nbrCellXList = [40, 40, 40]
nbrCellYList = [0, 12, 12]
nbrCellZList = [0, 0, 12]
nbDimsList = [1, 2, 3]
dxList = [0.1, 0.1, 0.1] # 1D, 2D and 3D cases
dyList = [0., 0.1, 0.1]
dzList = [0., 0., 0.1]
maxNbrDim = 3
baseName = 'gridIndexing'
outFilenameBase = os.path.join(path, baseName)
outFiles = []
for interpOrder in interpOrders:
filenames = [
outFilenameBase + '_' + str(dim) + 'd_O' + str(interpOrder) +
'.txt' for dim in nbDimsList
]
outFiles.append([open(f, 'w') for f in filenames])
for interpOrder, outFilesDim in zip(interpOrders, outFiles):
for dim, outFile, nbrCellX, nbrCellY, nbrCellZ, dx, dy, dz in zip(
nbDimsList, outFilesDim, nbrCellXList, nbrCellYList,
nbrCellZList, dxList, dyList, dzList):
params = IndexingParams(dim, interpOrder)
params.setNbrCell(nbrCellX, nbrCellY, nbrCellZ)
params.setDl(dx, dy, dz)
for quantity in quantities:
params.setIndexes(quantity, gl)
outString = "{} {} {} {} {} {} {}\n".format(
quantities.index(quantity), params.nbrCell, params.dl,
params.physicalStart, params.physicalEnd,
params.ghostStart, params.ghostEnd)
outFile.write(utilities.removeTupleFormat(outString))
for files in outFiles:
for f in files:
f.close()
def test_faraday_yee1D(path):
layout = gridlayout.GridLayout() # yee layout
tv = TestVariables()
By = np.zeros(layout.allocSize(tv.interpOrder, tv.ByCentering[0],
tv.nbrCells[0]),
dtype=np.float64)
Bz = np.zeros(layout.allocSize(tv.interpOrder, tv.BzCentering[0],
tv.nbrCells[0]),
dtype=np.float64)
Ey = np.zeros(layout.allocSize(tv.interpOrder, tv.EyCentering[0],
tv.nbrCells[0]),
dtype=np.float64)
Ez = np.zeros(layout.allocSize(tv.interpOrder, tv.EzCentering[0],
tv.nbrCells[0]),
dtype=np.float64)
ByNew = np.zeros(layout.allocSize(tv.interpOrder, tv.ByCentering[0],
tv.nbrCells[0]),
dtype=np.float64)
BzNew = np.zeros(layout.allocSize(tv.interpOrder, tv.BzCentering[0],
tv.nbrCells[0]),
dtype=np.float64)
psi_p_X = layout.physicalStartIndex(tv.interpOrder, 'primal')
pei_p_X = layout.physicalEndIndex(tv.interpOrder, 'primal', tv.nbrCells[0])
psi_d_X = layout.physicalStartIndex(tv.interpOrder, 'dual')
pei_d_X = layout.physicalEndIndex(tv.interpOrder, 'dual', tv.nbrCells[0])
nbrGhost_p = layout.nbrGhosts(tv.interpOrder, 'primal')
nbrGhost_d = layout.nbrGhosts(tv.interpOrder, 'dual')
x_primal = tv.meshSize[0] * np.arange(
layout.allocSize(tv.interpOrder, 'primal',
tv.nbrCells[0])) - tv.meshSize[0] * nbrGhost_p
x_dual = tv.meshSize[0] * np.arange(
layout.allocSize(tv.interpOrder, 'dual', tv.nbrCells[0])
) - tv.meshSize[0] * nbrGhost_d + tv.meshSize[0] * 0.5
Ey = np.cos(2 * np.pi / tv.domainSize[0] * x_primal)
Ez = np.sin(2 * np.pi / tv.domainSize[0] * x_primal)
By = np.tanh(x_dual - 0.5 * tv.domainSize[0])
Bz = np.tanh(x_dual - 0.5 * tv.domainSize[0])
ByNew[psi_d_X:pei_d_X + 1] = By[psi_d_X:pei_d_X + 1] + tv.dt * (
Ez[psi_p_X + 1:pei_p_X + 1] - Ez[psi_p_X:pei_p_X]) / tv.meshSize[0]
BzNew[psi_d_X:pei_d_X + 1] = Bz[psi_d_X:pei_d_X + 1] - tv.dt * (
Ey[psi_p_X + 1:pei_p_X + 1] - Ey[psi_p_X:pei_p_X]) / tv.meshSize[0]
filename_dbydt = "dbydt_yee_1D_order1.txt"
filename_dbzdt = "dbzdt_yee_1D_order1.txt"
np.savetxt(os.path.join(path, filename_dbydt), ByNew, delimiter=" ")
np.savetxt(os.path.join(path, filename_dbzdt), BzNew, delimiter=" ")
def fieldCoords(primalIndex, startIndex, quantity, direction, dl, origin):
halfCell = 0.
gl = gridlayout.GridLayout()
if gl.qtyCentering(quantity, direction) == 'dual':
halfCell = 0.5
x = ((primalIndex - startIndex) + halfCell) * dl + origin
return x
def test_deriv1D(path):
# derivative along X:
# By is dual in X, and derived along X it should lie on Ez
# Ez is primal in X, and derived along X it should lie on By
layout = gridlayout.GridLayout() # yee layout
tv = TestVariables()
for interpOrder in tv.interpOrders:
filename_dxBy = 'dxBy_interpOrder_{}_1d.txt'.format(interpOrder)
filename_dxEz = 'dxEz_interpOrder_{}_1d.txt'.format(interpOrder)
By = np.zeros(
layout.allocSize(interpOrder, tv.ByCentering[0], tv.nbrCells[0]))
Ez = np.zeros(
layout.allocSize(interpOrder, tv.EzCentering[0], tv.nbrCells[0]))
dxBy = np.zeros(layout.allocSizeDerived(interpOrder, tv.ByCentering[0],
tv.nbrCells[0]),
dtype=np.float64)
dxEz = np.zeros(layout.allocSizeDerived(interpOrder, tv.EzCentering[0],
tv.nbrCells[0]),
dtype=np.float64)
nbrGhost_p = layout.nbrGhosts(interpOrder, 'primal')
nbrGhost_d = layout.nbrGhosts(interpOrder, 'dual')
x_dual = tv.meshSize[0] * np.arange(
layout.allocSize(interpOrder, 'dual', tv.nbrCells[0])
) - tv.meshSize[0] * nbrGhost_d + tv.meshSize[0] * 0.5
x_primal = tv.meshSize[0] * np.arange(
layout.allocSize(interpOrder, 'primal',
tv.nbrCells[0])) - tv.meshSize[0] * nbrGhost_p
By = np.cos(2 * np.pi / tv.domainSize[0] * x_dual)
Ez = np.cos(2 * np.pi / tv.domainSize[0] * x_primal)
psi_d_X = layout.physicalStartIndex(interpOrder, 'dual')
pei_d_X = layout.physicalEndIndex(interpOrder, 'dual', tv.nbrCells[0])
psi_p_X = layout.physicalStartIndex(interpOrder, 'primal')
pei_p_X = layout.physicalEndIndex(interpOrder, 'primal',
tv.nbrCells[0])
dxBy[psi_p_X:pei_p_X +
1] = (By[psi_d_X:pei_d_X + 2] -
By[psi_d_X - 1:pei_d_X + 1]) / tv.meshSize[0]
dxEz[psi_d_X:pei_d_X + 1] = (Ez[psi_p_X + 1:pei_p_X + 1] -
Ez[psi_p_X:pei_p_X]) / tv.meshSize[0]
np.savetxt(os.path.join(path, filename_dxBy), dxBy, delimiter=" ")
np.savetxt(os.path.join(path, filename_dxEz), dxEz, delimiter=" ")
def test_ampere_yee1D(path):
layout = gridlayout.GridLayout() # yee layout
tv = TestVariables()
By = np.zeros(layout.allocSize(tv.interpOrder, tv.ByCentering[0],
tv.nbrCells[0]),
dtype=np.float64)
Bz = np.zeros(layout.allocSize(tv.interpOrder, tv.BzCentering[0],
tv.nbrCells[0]),
dtype=np.float64)
Jy = np.zeros(layout.allocSize(tv.interpOrder, tv.JyCentering[0],
tv.nbrCells[0]),
dtype=np.float64)
Jz = np.zeros(layout.allocSize(tv.interpOrder, tv.JzCentering[0],
tv.nbrCells[0]),
dtype=np.float64)
psi_p_X = layout.physicalStartIndex(tv.interpOrder, 'primal')
pei_p_X = layout.physicalEndIndex(tv.interpOrder, 'primal', tv.nbrCells[0])
psi_d_X = layout.physicalStartIndex(tv.interpOrder, 'dual')
pei_d_X = layout.physicalEndIndex(tv.interpOrder, 'dual', tv.nbrCells[0])
nbrGhost_p = layout.nbrGhosts(tv.interpOrder, 'primal')
nbrGhost_d = layout.nbrGhosts(tv.interpOrder, 'dual')
x_dual = tv.meshSize[0] * np.arange(
layout.allocSize(tv.interpOrder, 'dual', tv.nbrCells[0])
) - tv.meshSize[0] * nbrGhost_d + tv.meshSize[0] * 0.5
x_primal = tv.meshSize[0] * np.arange(
layout.allocSize(tv.interpOrder, 'primal',
tv.nbrCells[0])) - tv.meshSize[0] * nbrGhost_p
By = np.cos(2 * np.pi / tv.domainSize[0] * x_dual)
Bz = np.sin(2 * np.pi / tv.domainSize[0] * x_dual)
# Jy = -dxBz
# Jz = dxBy
Jy[psi_p_X:pei_p_X + 1] = -(Bz[psi_d_X:pei_d_X + 2] -
Bz[psi_d_X - 1:pei_d_X + 1]) / tv.meshSize[0]
Jz[psi_p_X:pei_p_X + 1] = (By[psi_d_X:pei_d_X + 2] -
By[psi_d_X - 1:pei_d_X + 1]) / tv.meshSize[0]
filename_jy = "jy_yee_1D_order1.txt"
filename_jz = "jz_yee_1D_order1.txt"
np.savetxt(os.path.join(path, filename_jy), Jy, delimiter=" ")
np.savetxt(os.path.join(path, filename_jz), Jz, delimiter=" ")
def main(path='./'):
if len(sys.argv) == 2:
path = sys.argv[1]
# TODO: refactor this for all python since they are the same
interpOrders = [1, 2, 3, 4]
nbDimsList = [1, 2, 3]
nbrCellXList = [40, 40, 40]
nbrCellYList = [0, 12, 12]
nbrCellZList = [0, 0, 12]
dxList = [0.01, 0.01, 0.01]
dyList = [0., 0.01, 0.01]
dzList = [0., 0., 0.01]
originPosition = [0., 0., 0.]
gl = gridlayout.GridLayout()
# TODO : end Todo
# TODO: FieldCoords and CenteredCoords share a common base, refactor this
baseNameSummary = "fieldCoords_summary"
baseNameValues = "fieldCoords_values"
outFilenameBaseSummary = os.path.join(path, baseNameSummary)
outFilenameBaseValues = os.path.join(path, baseNameValues)
outSummaries = []
outValues = []
for interpOrder in interpOrders:
filenamesSum = [
outFilenameBaseSummary + '_' + str(dim) + 'd_O' +
str(interpOrder) + '.txt' for dim in nbDimsList
]
filenamesVal = [
outFilenameBaseValues + '_' + str(dim) + 'd_O' + str(interpOrder) +
'.txt' for dim in nbDimsList
]
outSummaries.append([open(f, 'w') for f in filenamesSum])
outValues.append([open(f, 'w') for f in filenamesVal])
for interpOrder, outFilesSumDim, outFilesValDim in zip(
interpOrders, outSummaries, outValues):
for dimension,outFileS, outFileV,nbrCellX,nbrCellY,\
nbrCellZ,dx,dy,dz in zip(nbDimsList, outFilesSumDim, outFilesValDim,
nbrCellXList,nbrCellYList,
nbrCellZList,dxList,dyList,
dzList):
for quantity in gl.hybridQuantities:
params = FieldNodeCoordParams(dimension, interpOrder)
params.setNbrCell(nbrCellX, nbrCellY, nbrCellZ)
params.setDl(dx, dy, dz)
centering = getQtyCentering(gl, quantity, dimension)
params.setCoord(gl, originPosition, centering)
summaryBasePart = "{} {} {} ".format(quantity, params.nbrCell,
params.dl)
summaryGridLayoutPart = "{} {} {}\n".format(
params.iStart, params.iEnd, params.origin)
outSummaryString = summaryBasePart + summaryGridLayoutPart
outSummaryString = utilities.removeTupleFormat(
outSummaryString)
outFileS.write(outSummaryString)
if dimension == 1:
for position in np.arange(params.iStart, params.iEnd + 1):
outValuesString = "{} {} {}\n".format(
quantity, position,
fieldCoords(position, params.iStart, quantity, 'X',
params.dl, params.origin))
outFileV.write(
utilities.removeTupleFormat(outValuesString))
elif dimension == 2:
for positionX in np.arange(params.iStart[0],
params.iEnd[0] + 1):
for positionY in np.arange(params.iStart[1],
params.iEnd[1] + 1):
position = (positionX, positionY)
centered = (fieldCoords(positionX,
params.iStart[0], quantity,
'X', params.dl[0],
params.origin[0]),
fieldCoords(positionY,
params.iStart[1], quantity,
'Y', params.dl[1],
params.origin[1]))
outValuesString = "{} {} {}\n".format(
quantity, position, centered)
outFileV.write(
utilities.removeTupleFormat(outValuesString))
elif dimension == 3:
for positionX in np.arange(params.iStart[0],
params.iEnd[0] + 1):
for positionY in np.arange(params.iStart[1],
params.iEnd[1] + 1):
for positionZ in np.arange(params.iStart[2],
params.iEnd[2] + 1):
position = (positionX, positionY, positionZ)
centered = (fieldCoords(
positionX, params.iStart[0], quantity, 'X',
params.dl[0], params.origin[0]),
fieldCoords(
positionY, params.iStart[1],
quantity, 'Y', params.dl[1],
params.origin[1]),
fieldCoords(
positionZ, params.iStart[2],
quantity, 'Z', params.dl[2],
params.origin[2]))
outValuesString = "{} {} {}\n".format(
quantity, position, centered)
outFileV.write(
utilities.removeTupleFormat(
outValuesString))
for outFilesSumDim, outFilesValDim in zip(outSummaries, outValues):
for f1, f2 in zip(outFilesSumDim, outFilesValDim):
f1.close()
f2.close()
def main(path='./'):
if len(sys.argv) == 2:
path = sys.argv[1]
# TODO: refactor this for all python since they are the same
interpOrders = [1,2,3]
nbDimsList= [1]#, 2, 3]
nbrCellXList=[40, 40, 40]
nbrCellYList=[ 0, 12, 12]
nbrCellZList=[ 0, 0, 12]
dxList=[0.01, 0.01, 0.01]
dyList=[0. , 0.01, 0.01]
dzList=[0. , 0. , 0.01]
originPosition = [0., 0., 0.]
gl = gridlayout.GridLayout()
# TODO : end Todo
# TODO: FieldCoords and CenteredCoords share a common base, refactor this
outSummary1D = open(os.path.join(path,"deriv_summary_1d.txt"), "w")
outSummary2D = open(os.path.join(path,"deriv_summary_2d.txt"), "w")
outSummary3D = open(os.path.join(path,"deriv_summary_3d.txt"), "w")
outSummaries =[outSummary1D, outSummary2D, outSummary3D]
outActualValues1D = open(os.path.join(path,"deriv_values_1d.txt"), "w")
outActualValues2D = open(os.path.join(path,"deriv_values_2d.txt"), "w")
outActualValues3D = open(os.path.join(path,"deriv_values_3d.txt"), "w")
outActualValuesFiles = [outActualValues1D, outActualValues2D, outActualValues3D]
outDerivedValues1D = open(os.path.join(path, "deriv_derived_values_1d.txt"),"w")
for interpOrder in interpOrders:
for dimension,outSummary, outValues,nbrCellX,nbrCellY,\
nbrCellZ,dx,dy,dz in zip(nbDimsList, outSummaries,
outActualValuesFiles,
nbrCellXList,nbrCellYList,
nbrCellZList,dxList,dyList,
dzList):
# TODO : the association depend on the direction
# Here we derive in the direction X
quantities = ('Ex','Ey')
derivedQuantities = ('rho','Bz')
for quantity,derivQuantity in zip(quantities, derivedQuantities):
params = DerivParams(dimension,interpOrder);
params.setNbrCell(nbrCellX,nbrCellY,nbrCellZ)
params.setDl(dx,dy,dz)
centering = fieldNodeCoordinates.getQtyCentering(gl,quantity,dimension)
derivedCentering = fieldNodeCoordinates.getQtyCentering(gl, derivQuantity, dimension)
params.setCoord(gl, originPosition, centering, derivedCentering)
summaryBasePart = "{} {} {} {} {} ".format(
params.interpOrder,
quantity,
derivQuantity,
params.nbrCell,
params.dl)
summaryGridLayoutPart = " {} {} {} {} {}\n".format(
params.iGhostStart,
params.iGhostEnd,
params.iStart,
params.iEnd,
params.origin)
outSummaryString = summaryBasePart + summaryGridLayoutPart
outSummaryString = utilities.removeTupleFormat(outSummaryString)
outSummary.write(outSummaryString)
if dimension == 1:
for position in np.arange(params.iGhostStart, params.iGhostEnd ):
coord = fieldNodeCoordinates.fieldCoords(position, params.iStart,quantity,'X',params.dl, params.origin)
functionValue = primitive(coord)
outValuesString = "{} {} {} {}\n".format(
params.interpOrder,
quantity,
position,
functionValue,
)
outValues.write(utilities.removeTupleFormat(outValuesString))
for position in np.arange(params.iStart, params.iEnd + 1 ):
coord = fieldNodeCoordinates.fieldCoords(position, params.iStart,derivQuantity,'X',params.dl, params.origin)
derivedValue = scipy.misc.derivative(primitive,coord,dx,order=3)
outDerivedValuesString = "{} {} {} {}\n".format(
params.interpOrder,
derivQuantity,
position,
derivedValue
)
outDerivedValues1D.write(utilities.removeTupleFormat(outDerivedValuesString))
for outSummary,outValues in zip(outSummaries, outActualValuesFiles):
outSummary.close()
outValues.close()
outDerivedValues1D.close()
def test_faraday_yee3D(path):
layout = gridlayout.GridLayout() # yee layout
tv = TestVariables()
Bx = np.zeros([
layout.allocSize(tv.interpOrder, tv.BxCentering[0], tv.nbrCells[0]),
layout.allocSize(tv.interpOrder, tv.BxCentering[1], tv.nbrCells[1]),
layout.allocSize(tv.interpOrder, tv.BxCentering[2], tv.nbrCells[2])
],
dtype=np.float64)
By = np.zeros([
layout.allocSize(tv.interpOrder, tv.ByCentering[0], tv.nbrCells[0]),
layout.allocSize(tv.interpOrder, tv.ByCentering[1], tv.nbrCells[1]),
layout.allocSize(tv.interpOrder, tv.ByCentering[2], tv.nbrCells[2])
],
dtype=np.float64)
Bz = np.zeros([
layout.allocSize(tv.interpOrder, tv.BzCentering[0], tv.nbrCells[0]),
layout.allocSize(tv.interpOrder, tv.BzCentering[1], tv.nbrCells[1]),
layout.allocSize(tv.interpOrder, tv.BzCentering[2], tv.nbrCells[2])
],
dtype=np.float64)
Ex = np.zeros([
layout.allocSize(tv.interpOrder, tv.ExCentering[0], tv.nbrCells[0]),
layout.allocSize(tv.interpOrder, tv.ExCentering[1], tv.nbrCells[1]),
layout.allocSize(tv.interpOrder, tv.ExCentering[2], tv.nbrCells[2])
],
dtype=np.float64)
Ey = np.zeros([
layout.allocSize(tv.interpOrder, tv.EyCentering[0], tv.nbrCells[0]),
layout.allocSize(tv.interpOrder, tv.EyCentering[1], tv.nbrCells[1]),
layout.allocSize(tv.interpOrder, tv.EyCentering[2], tv.nbrCells[2])
],
dtype=np.float64)
Ez = np.zeros([
layout.allocSize(tv.interpOrder, tv.EzCentering[0], tv.nbrCells[0]),
layout.allocSize(tv.interpOrder, tv.EzCentering[1], tv.nbrCells[1]),
layout.allocSize(tv.interpOrder, tv.EzCentering[2], tv.nbrCells[2])
],
dtype=np.float64)
BxNew = np.zeros([
layout.allocSize(tv.interpOrder, tv.BxCentering[0], tv.nbrCells[0]),
layout.allocSize(tv.interpOrder, tv.BxCentering[1], tv.nbrCells[1]),
layout.allocSize(tv.interpOrder, tv.BxCentering[2], tv.nbrCells[2])
],
dtype=np.float64)
ByNew = np.zeros([
layout.allocSize(tv.interpOrder, tv.ByCentering[0], tv.nbrCells[0]),
layout.allocSize(tv.interpOrder, tv.ByCentering[1], tv.nbrCells[1]),
layout.allocSize(tv.interpOrder, tv.ByCentering[2], tv.nbrCells[2])
],
dtype=np.float64)
BzNew = np.zeros([
layout.allocSize(tv.interpOrder, tv.BzCentering[0], tv.nbrCells[0]),
layout.allocSize(tv.interpOrder, tv.BzCentering[1], tv.nbrCells[1]),
layout.allocSize(tv.interpOrder, tv.BzCentering[2], tv.nbrCells[2])
],
dtype=np.float64)
u1 = np.zeros_like(BxNew)
u2 = np.zeros_like(BxNew)
v1 = np.zeros_like(ByNew)
v2 = np.zeros_like(ByNew)
w1 = np.zeros_like(BzNew)
w2 = np.zeros_like(BzNew)
psi_p_X = layout.physicalStartIndex(tv.interpOrder, 'primal')
pei_p_X = layout.physicalEndIndex(tv.interpOrder, 'primal', tv.nbrCells[0])
psi_p_Y = layout.physicalStartIndex(tv.interpOrder, 'primal')
pei_p_Y = layout.physicalEndIndex(tv.interpOrder, 'primal', tv.nbrCells[1])
psi_p_Z = layout.physicalStartIndex(tv.interpOrder, 'primal')
pei_p_Z = layout.physicalEndIndex(tv.interpOrder, 'primal', tv.nbrCells[2])
psi_d_X = layout.physicalStartIndex(tv.interpOrder, 'dual')
pei_d_X = layout.physicalEndIndex(tv.interpOrder, 'dual', tv.nbrCells[0])
psi_d_Y = layout.physicalStartIndex(tv.interpOrder, 'dual')
pei_d_Y = layout.physicalEndIndex(tv.interpOrder, 'dual', tv.nbrCells[1])
psi_d_Z = layout.physicalStartIndex(tv.interpOrder, 'dual')
pei_d_Z = layout.physicalEndIndex(tv.interpOrder, 'dual', tv.nbrCells[2])
nbrGhost_p = layout.nbrGhosts(tv.interpOrder, 'primal')
nbrGhost_d = layout.nbrGhosts(tv.interpOrder, 'dual')
x_primal = tv.meshSize[0] * np.arange(
layout.allocSize(tv.interpOrder, 'primal',
tv.nbrCells[0])) - tv.meshSize[0] * nbrGhost_p
y_primal = tv.meshSize[1] * np.arange(
layout.allocSize(tv.interpOrder, 'primal',
tv.nbrCells[1])) - tv.meshSize[1] * nbrGhost_p
z_primal = tv.meshSize[2] * np.arange(
layout.allocSize(tv.interpOrder, 'primal',
tv.nbrCells[2])) - tv.meshSize[2] * nbrGhost_p
x_dual = tv.meshSize[0] * np.arange(
layout.allocSize(tv.interpOrder, 'dual', tv.nbrCells[0])
) - tv.meshSize[0] * nbrGhost_d + tv.meshSize[0] * 0.5
y_dual = tv.meshSize[1] * np.arange(
layout.allocSize(tv.interpOrder, 'dual', tv.nbrCells[1])
) - tv.meshSize[1] * nbrGhost_d + tv.meshSize[1] * 0.5
z_dual = tv.meshSize[2] * np.arange(
layout.allocSize(tv.interpOrder, 'dual', tv.nbrCells[2])
) - tv.meshSize[2] * nbrGhost_d + tv.meshSize[2] * 0.5
Ex = np.tensordot(np.sin(2 * np.pi / tv.domainSize[0] * x_dual),
np.tensordot(
np.cos(2 * np.pi / tv.domainSize[1] * y_primal),
np.tanh(2 * np.pi / tv.domainSize[2] * z_primal),
axes=0),
axes=0)
Ey = np.tensordot(np.tanh(2 * np.pi / tv.domainSize[0] * x_primal),
np.tensordot(
np.sin(2 * np.pi / tv.domainSize[1] * y_dual),
np.cos(2 * np.pi / tv.domainSize[2] * z_primal),
axes=0),
axes=0)
Ez = np.tensordot(np.cos(2 * np.pi / tv.domainSize[0] * x_primal),
np.tensordot(
np.tanh(2 * np.pi / tv.domainSize[1] * y_primal),
np.sin(2 * np.pi / tv.domainSize[2] * z_dual),
axes=0),
axes=0)
Bx = np.tensordot(np.tanh(x_primal - 0.5 * tv.domainSize[0]),
np.tensordot(np.tanh(y_dual - 0.5 * tv.domainSize[1]),
np.tanh(z_dual - 0.5 * tv.domainSize[2]),
axes=0),
axes=0)
By = np.tensordot(np.tanh(x_dual - 0.5 * tv.domainSize[0]),
np.tensordot(np.tanh(y_primal - 0.5 * tv.domainSize[1]),
np.tanh(z_dual - 0.5 * tv.domainSize[2]),
axes=0),
axes=0)
Bz = np.tensordot(np.tanh(x_dual - 0.5 * tv.domainSize[0]),
np.tensordot(np.tanh(y_dual - 0.5 * tv.domainSize[1]),
np.tanh(z_primal - 0.5 * tv.domainSize[2]),
axes=0),
axes=0)
u1[:, psi_d_Y:pei_d_Y +
1, :] = -tv.dt * (Ez[:, psi_p_Y + 1:pei_p_Y + 1, :] -
Ez[:, psi_p_Y:pei_p_Y, :]) / tv.meshSize[1]
u2[:, :, psi_d_Z:pei_d_Z +
1] = +tv.dt * (Ey[:, :, psi_p_Z + 1:pei_p_Z + 1] -
Ey[:, :, psi_p_Z:pei_p_Z]) / tv.meshSize[2]
BxNew = Bx + u1 + u2
v1[:, :, psi_d_Z:pei_d_Z +
1] = -tv.dt * (Ex[:, :, psi_p_Z + 1:pei_p_Z + 1] -
Ex[:, :, psi_p_Z:pei_p_Z]) / tv.meshSize[2]
v2[psi_d_X:pei_d_X +
1, :, :] = +tv.dt * (Ez[psi_p_X + 1:pei_p_X + 1, :, :] -
Ez[psi_p_X:pei_p_X, :, :]) / tv.meshSize[0]
ByNew = By + v1 + v2
w1[psi_d_X:pei_d_X +
1, :, :] = -tv.dt * (Ey[psi_p_X + 1:pei_p_X + 1, :, :] -
Ey[psi_p_X:pei_p_X, :, :]) / tv.meshSize[0]
w2[:, psi_d_Y:pei_d_Y +
1, :] = +tv.dt * (Ex[:, psi_p_Y + 1:pei_p_Y + 1, :] -
Ex[:, psi_p_Y:pei_p_Y, :]) / tv.meshSize[1]
BzNew = Bz + w1 + w2
filename_dbxdt = "dbxdt_yee_3D_order1.txt"
filename_dbydt = "dbydt_yee_3D_order1.txt"
filename_dbzdt = "dbzdt_yee_3D_order1.txt"
np.savetxt(os.path.join(path, filename_dbxdt),
BxNew.flatten('C'),
delimiter=" ")
np.savetxt(os.path.join(path, filename_dbydt),
ByNew.flatten('C'),
delimiter=" ")
np.savetxt(os.path.join(path, filename_dbzdt),
BzNew.flatten('C'),
delimiter=" ")
def test_laplacian_yee1D(path):
layout = gridlayout.GridLayout() # yee layout
tv = TestVariables()
for interpOrder in tv.interpOrders:
Jx = np.zeros(layout.allocSize(interpOrder, tv.JxCentering[0],
tv.nbrCells[0]),
dtype=np.float64)
Jy = np.zeros(layout.allocSize(interpOrder, tv.JyCentering[0],
tv.nbrCells[0]),
dtype=np.float64)
Jz = np.zeros(layout.allocSize(interpOrder, tv.JzCentering[0],
tv.nbrCells[0]),
dtype=np.float64)
lapJx = np.zeros(layout.allocSize(interpOrder, tv.JxCentering[0],
tv.nbrCells[0]),
dtype=np.float64)
lapJy = np.zeros(layout.allocSize(interpOrder, tv.JyCentering[0],
tv.nbrCells[0]),
dtype=np.float64)
lapJz = np.zeros(layout.allocSize(interpOrder, tv.JzCentering[0],
tv.nbrCells[0]),
dtype=np.float64)
psi_p_X = layout.physicalStartIndex(interpOrder, 'primal')
pei_p_X = layout.physicalEndIndex(interpOrder, 'primal',
tv.nbrCells[0])
psi_d_X = layout.physicalStartIndex(interpOrder, 'dual')
pei_d_X = layout.physicalEndIndex(interpOrder, 'dual', tv.nbrCells[0])
nbrGhost_p = layout.nbrGhosts(interpOrder, 'primal')
nbrGhost_d = layout.nbrGhosts(interpOrder, 'dual')
x_primal = tv.meshSize[0] * np.arange(
layout.allocSize(interpOrder, 'primal',
tv.nbrCells[0])) - tv.meshSize[0] * nbrGhost_p
x_dual = tv.meshSize[0] * np.arange(
layout.allocSize(interpOrder, 'dual', tv.nbrCells[0])
) - tv.meshSize[0] * nbrGhost_d + tv.meshSize[0] * 0.5
Jx = np.sinh(0.1 * x_dual)
Jy = np.sinh(0.3 * x_primal)
Jz = np.sinh(0.2 * x_primal)
lapJx[psi_d_X:pei_d_X + 1] = (
Jx[psi_d_X + 1:pei_d_X + 2] - 2.0 * Jx[psi_d_X:pei_d_X + 1] +
Jx[psi_d_X - 1:pei_d_X]) / (tv.meshSize[0] * tv.meshSize[0])
lapJy[psi_p_X:pei_p_X + 1] = (
Jy[psi_p_X + 1:pei_p_X + 2] - 2.0 * Jy[psi_p_X:pei_p_X + 1] +
Jy[psi_p_X - 1:pei_p_X]) / (tv.meshSize[0] * tv.meshSize[0])
lapJz[psi_p_X:pei_p_X + 1] = (
Jz[psi_p_X + 1:pei_p_X + 2] - 2.0 * Jz[psi_p_X:pei_p_X + 1] +
Jz[psi_p_X - 1:pei_p_X]) / (tv.meshSize[0] * tv.meshSize[0])
filename_lapJx = 'lapJx_interpOrder_{}_1d.txt'.format(interpOrder)
filename_lapJy = 'lapJy_interpOrder_{}_1d.txt'.format(interpOrder)
filename_lapJz = 'lapJz_interpOrder_{}_1d.txt'.format(interpOrder)
np.savetxt(os.path.join(path, filename_lapJx), lapJx, delimiter=" ")
np.savetxt(os.path.join(path, filename_lapJy), lapJy, delimiter=" ")
np.savetxt(os.path.join(path, filename_lapJz), lapJz, delimiter=" ")
def test_laplacian_yee3D(path):
layout = gridlayout.GridLayout() # yee layout
tv = TestVariables()
for interpOrder in tv.interpOrders:
Jx = np.zeros([
layout.allocSize(interpOrder, tv.JxCentering[0], tv.nbrCells[0]),
layout.allocSize(interpOrder, tv.JxCentering[1], tv.nbrCells[1]),
layout.allocSize(interpOrder, tv.JxCentering[2], tv.nbrCells[2])
],
dtype=np.float64)
Jy = np.zeros([
layout.allocSize(interpOrder, tv.JyCentering[0], tv.nbrCells[0]),
layout.allocSize(interpOrder, tv.JyCentering[1], tv.nbrCells[1]),
layout.allocSize(interpOrder, tv.JyCentering[2], tv.nbrCells[2])
],
dtype=np.float64)
Jz = np.zeros([
layout.allocSize(interpOrder, tv.JzCentering[0], tv.nbrCells[0]),
layout.allocSize(interpOrder, tv.JzCentering[1], tv.nbrCells[1]),
layout.allocSize(interpOrder, tv.JzCentering[2], tv.nbrCells[2])
],
dtype=np.float64)
Jx_x = np.zeros_like(Jx)
Jx_y = np.zeros_like(Jx)
Jx_z = np.zeros_like(Jx)
Jy_x = np.zeros_like(Jy)
Jy_y = np.zeros_like(Jy)
Jy_z = np.zeros_like(Jy)
Jz_x = np.zeros_like(Jz)
Jz_y = np.zeros_like(Jz)
Jz_z = np.zeros_like(Jz)
lapJx = np.zeros([
layout.allocSize(interpOrder, tv.JxCentering[0], tv.nbrCells[0]),
layout.allocSize(interpOrder, tv.JxCentering[1], tv.nbrCells[1]),
layout.allocSize(interpOrder, tv.JxCentering[2], tv.nbrCells[2])
],
dtype=np.float64)
lapJy = np.zeros([
layout.allocSize(interpOrder, tv.JyCentering[0], tv.nbrCells[0]),
layout.allocSize(interpOrder, tv.JyCentering[1], tv.nbrCells[1]),
layout.allocSize(interpOrder, tv.JyCentering[2], tv.nbrCells[2])
],
dtype=np.float64)
lapJz = np.zeros([
layout.allocSize(interpOrder, tv.JzCentering[0], tv.nbrCells[0]),
layout.allocSize(interpOrder, tv.JzCentering[1], tv.nbrCells[1]),
layout.allocSize(interpOrder, tv.JzCentering[2], tv.nbrCells[2])
],
dtype=np.float64)
psi_p_X = layout.physicalStartIndex(interpOrder, 'primal')
pei_p_X = layout.physicalEndIndex(interpOrder, 'primal',
tv.nbrCells[0])
psi_p_Y = layout.physicalStartIndex(interpOrder, 'primal')
pei_p_Y = layout.physicalEndIndex(interpOrder, 'primal',
tv.nbrCells[1])
psi_p_Z = layout.physicalStartIndex(interpOrder, 'primal')
pei_p_Z = layout.physicalEndIndex(interpOrder, 'primal',
tv.nbrCells[2])
psi_d_X = layout.physicalStartIndex(interpOrder, 'dual')
pei_d_X = layout.physicalEndIndex(interpOrder, 'dual', tv.nbrCells[0])
psi_d_Y = layout.physicalStartIndex(interpOrder, 'dual')
pei_d_Y = layout.physicalEndIndex(interpOrder, 'dual', tv.nbrCells[1])
psi_d_Z = layout.physicalStartIndex(interpOrder, 'dual')
pei_d_Z = layout.physicalEndIndex(interpOrder, 'dual', tv.nbrCells[2])
nbrGhost_p = layout.nbrGhosts(interpOrder, 'primal')
nbrGhost_d = layout.nbrGhosts(interpOrder, 'dual')
x_primal = tv.meshSize[0] * np.arange(
layout.allocSize(interpOrder, 'primal',
tv.nbrCells[0])) - tv.meshSize[0] * nbrGhost_p
x_dual = tv.meshSize[0] * np.arange(
layout.allocSize(interpOrder, 'dual', tv.nbrCells[0])
) - tv.meshSize[0] * nbrGhost_d + tv.meshSize[0] * 0.5
y_primal = tv.meshSize[1] * np.arange(
layout.allocSize(interpOrder, 'primal',
tv.nbrCells[1])) - tv.meshSize[1] * nbrGhost_p
y_dual = tv.meshSize[1] * np.arange(
layout.allocSize(interpOrder, 'dual', tv.nbrCells[1])
) - tv.meshSize[1] * nbrGhost_d + tv.meshSize[1] * 0.5
z_primal = tv.meshSize[2] * np.arange(
layout.allocSize(interpOrder, 'primal',
tv.nbrCells[2])) - tv.meshSize[2] * nbrGhost_p
z_dual = tv.meshSize[2] * np.arange(
layout.allocSize(interpOrder, 'dual', tv.nbrCells[2])
) - tv.meshSize[2] * nbrGhost_d + tv.meshSize[2] * 0.5
Jx = np.tensordot(np.sinh(0.1 * x_dual),
np.tensordot(np.cosh(0.1 * y_primal),
np.tanh(0.1 * z_primal),
axes=0),
axes=0)
Jy = np.tensordot(np.sinh(0.3 * x_primal),
np.tensordot(np.cosh(0.3 * y_dual),
np.tanh(0.3 * z_primal),
axes=0),
axes=0)
Jz = np.tensordot(np.sinh(0.2 * x_primal),
np.tensordot(np.cosh(0.2 * y_primal),
np.tanh(0.2 * z_dual),
axes=0),
axes=0)
Jx_x[psi_d_X:pei_d_X +
1, :, :] = (Jx[psi_d_X + 1:pei_d_X + 2, :, :] -
2.0 * Jx[psi_d_X:pei_d_X + 1, :, :] +
Jx[psi_d_X - 1:pei_d_X, :, :]) / (tv.meshSize[0] *
tv.meshSize[0])
Jx_y[:, psi_p_Y:pei_p_Y +
1, :] = (Jx[:, psi_p_Y + 1:pei_p_Y + 2, :] -
2.0 * Jx[:, psi_p_Y:pei_p_Y + 1, :] +
Jx[:, psi_p_Y - 1:pei_p_Y, :]) / (tv.meshSize[1] *
tv.meshSize[1])
Jx_z[:, :, psi_p_Z:pei_p_Z +
1] = (Jx[:, :, psi_p_Z + 1:pei_p_Z + 2] -
2.0 * Jx[:, :, psi_p_Z:pei_p_Z + 1] +
Jx[:, :, psi_p_Z - 1:pei_p_Z]) / (tv.meshSize[2] *
tv.meshSize[2])
Jy_x[psi_p_X:pei_p_X +
1, :, :] = (Jy[psi_p_X + 1:pei_p_X + 2, :, :] -
2.0 * Jy[psi_p_X:pei_p_X + 1, :, :] +
Jy[psi_p_X - 1:pei_p_X, :, :]) / (tv.meshSize[0] *
tv.meshSize[0])
Jy_y[:, psi_d_Y:pei_d_Y +
1, :] = (Jy[:, psi_d_Y + 1:pei_d_Y + 2, :] -
2.0 * Jy[:, psi_d_Y:pei_d_Y + 1, :] +
Jy[:, psi_d_Y - 1:pei_d_Y, :]) / (tv.meshSize[1] *
tv.meshSize[1])
Jy_z[:, :, psi_p_Z:pei_p_Z +
1] = (Jy[:, :, psi_p_Z + 1:pei_p_Z + 2] -
2.0 * Jy[:, :, psi_p_Z:pei_p_Z + 1] +
Jy[:, :, psi_p_Z - 1:pei_p_Z]) / (tv.meshSize[2] *
tv.meshSize[2])
Jz_x[psi_p_X:pei_p_X +
1, :, :] = (Jz[psi_p_X + 1:pei_p_X + 2, :, :] -
2.0 * Jz[psi_p_X:pei_p_X + 1, :, :] +
Jz[psi_p_X - 1:pei_p_X, :, :]) / (tv.meshSize[0] *
tv.meshSize[0])
Jz_y[:, psi_p_Y:pei_p_Y +
1, :] = (Jz[:, psi_p_Y + 1:pei_p_Y + 2, :] -
2.0 * Jz[:, psi_p_Y:pei_p_Y + 1, :] +
Jz[:, psi_p_Y - 1:pei_p_Y, :]) / (tv.meshSize[1] *
tv.meshSize[1])
Jz_z[:, :, psi_d_Z:pei_d_Z +
1] = (Jz[:, :, psi_d_Z + 1:pei_d_Z + 2] -
2.0 * Jz[:, :, psi_d_Z:pei_d_Z + 1] +
Jz[:, :, psi_d_Z - 1:pei_d_Z]) / (tv.meshSize[2] *
tv.meshSize[2])
lapJx = Jx_x + Jx_y + Jx_z
lapJy = Jy_x + Jy_y + Jy_z
lapJz = Jz_x + Jz_y + Jz_z
filename_lapJx = 'lapJx_interpOrder_{}_3d.txt'.format(interpOrder)
filename_lapJy = 'lapJy_interpOrder_{}_3d.txt'.format(interpOrder)
filename_lapJz = 'lapJz_interpOrder_{}_3d.txt'.format(interpOrder)
np.savetxt(os.path.join(path, filename_lapJx),
lapJx.flatten('C'),
delimiter=" ")
np.savetxt(os.path.join(path, filename_lapJy),
lapJy.flatten('C'),
delimiter=" ")
np.savetxt(os.path.join(path, filename_lapJz),
lapJz.flatten('C'),
delimiter=" ")
def main(path='./'):
if len(sys.argv) == 2:
path = sys.argv[1]
interpOrders = [1, 2, 3, 4]
nbDimsList = [1, 2, 3]
nbrCellXList = [40, 40, 40]
nbrCellYList = [0, 12, 12]
nbrCellZList = [0, 0, 12]
dxList = [0.1, 0.1, 0.1]
dyList = [0., 0.1, 0.1]
dzList = [0., 0., 0.1]
originPosition = [0., 0., 0.]
gl = gridlayout.GridLayout()
# ------- Debug commands -------
# for icase in icase_l:
# idim = dim_l[icase]
# order = interpOrder_l[icase]
# print( "Interpolation order = %d" % order )
# print( "Nbr of cells = %d" % nbrCells[Direction_l[idim][1]][icase])
# print( "Nbr of ghost cells on the primal mesh = %d on each side" %
# gl.nbrGhostsPrimal(order) )
# ------------------------------
baseNameSummary = "centeredCoords_summary"
baseNameValues = "centeredCoords_values"
outFilenameBaseSummary = os.path.join(path, baseNameSummary)
outFilenameBaseValues = os.path.join(path, baseNameValues)
outSummaries = []
outValues = []
for interpOrder in interpOrders:
filenamesSum = [
outFilenameBaseSummary + '_' + str(dim) + 'd_O' +
str(interpOrder) + '.txt' for dim in nbDimsList
]
filenamesVal = [
outFilenameBaseValues + '_' + str(dim) + 'd_O' + str(interpOrder) +
'.txt' for dim in nbDimsList
]
outSummaries.append([open(f, 'w') for f in filenamesSum])
outValues.append([open(f, 'w') for f in filenamesVal])
for interpOrder, outFilesSumDim, outFilesValDim in zip(
interpOrders, outSummaries, outValues):
for dimension,outFileS, outFileV,nbrCellX,nbrCellY,\
nbrCellZ,dx,dy,dz in zip(nbDimsList, outFilesSumDim, outFilesValDim,
nbrCellXList,nbrCellYList,
nbrCellZList,dxList,dyList,
dzList):
params = CenteredCoordParams(dimension, interpOrder)
params.setNbrCell(nbrCellX, nbrCellY, nbrCellZ)
params.setDl(dx, dy, dz)
centering = getCellCentered(dimension)
params.setCoord(gl, originPosition, centering)
summaryBasePart = "{} {} ".format(params.nbrCell, params.dl)
summaryGridLayoutPart = "{} {} {}\n".format(
params.iStart, params.iEnd, params.origin)
outSummaryString = summaryBasePart + summaryGridLayoutPart
outSummaryString = utilities.removeTupleFormat(outSummaryString)
outFileS.write(outSummaryString)
if dimension == 1:
for position in np.arange(params.iStart, params.iEnd + 1):
outValuesString = "{} {}\n".format(
position,
centeredCoords(position, params.iStart, params.dl,
params.origin))
outFileV.write(
utilities.removeTupleFormat(outValuesString))
elif dimension == 2:
for positionX in np.arange(params.iStart[0],
params.iEnd[0] + 1):
for positionY in np.arange(params.iStart[1],
params.iEnd[1] + 1):
position = (positionX, positionY)
centered = (centeredCoords(positionX, params.iStart[0],
params.dl[0],
params.origin[0]),
centeredCoords(positionY, params.iStart[1],
params.dl[1],
params.origin[1]))
outValuesString = "{} {}\n".format(position, centered)
outFileV.write(
utilities.removeTupleFormat(outValuesString))
elif dimension == 3:
for positionX in np.arange(params.iStart[0],
params.iEnd[0] + 1):
for positionY in np.arange(params.iStart[1],
params.iEnd[1] + 1):
for positionZ in np.arange(params.iStart[2],
params.iEnd[2] + 1):
position = (positionX, positionY, positionZ)
centered = (centeredCoords(positionX,
params.iStart[0],
params.dl[0],
params.origin[0]),
centeredCoords(positionY,
params.iStart[1],
params.dl[1],
params.origin[1]),
centeredCoords(positionZ,
params.iStart[2],
params.dl[2],
params.origin[2]))
outValuesString = "{} {}\n".format(
position, centered)
outFileV.write(
utilities.removeTupleFormat(outValuesString))
for outFilesSumDim, outFilesValDim in zip(outSummaries, outValues):
for f1, f2 in zip(outFilesSumDim, outFilesValDim):
f1.close()
f2.close()
def test_deriv2D(path):
layout = gridlayout.GridLayout() # yee layout
tv = TestVariables()
for interpOrder in tv.interpOrders:
filename_dxBy = 'dxBy_interpOrder_{}_2d.txt'.format(interpOrder)
filename_dyBy = 'dyBy_interpOrder_{}_2d.txt'.format(interpOrder)
filename_dxEz = 'dxEz_interpOrder_{}_2d.txt'.format(interpOrder)
filename_dyEz = 'dyEz_interpOrder_{}_2d.txt'.format(interpOrder)
By = np.zeros([
layout.allocSize(interpOrder, tv.ByCentering[0], tv.nbrCells[0]),
layout.allocSize(interpOrder, tv.ByCentering[1], tv.nbrCells[1])
],
dtype=np.float64)
Ez = np.zeros([
layout.allocSize(interpOrder, tv.EzCentering[0], tv.nbrCells[0]),
layout.allocSize(interpOrder, tv.EzCentering[1], tv.nbrCells[1])
],
dtype=np.float64)
dxBy = np.zeros([
layout.allocSizeDerived(interpOrder, tv.ByCentering[0],
tv.nbrCells[0]),
layout.allocSize(interpOrder, tv.ByCentering[1], tv.nbrCells[1])
],
dtype=np.float64)
dyBy = np.zeros([
layout.allocSize(interpOrder, tv.ByCentering[0], tv.nbrCells[0]),
layout.allocSizeDerived(interpOrder, tv.ByCentering[1],
tv.nbrCells[1])
],
dtype=np.float64)
dxEz = np.zeros([
layout.allocSizeDerived(interpOrder, tv.EzCentering[0],
tv.nbrCells[0]),
layout.allocSize(interpOrder, tv.EzCentering[1], tv.nbrCells[1])
],
dtype=np.float64)
dyEz = np.zeros([
layout.allocSize(interpOrder, tv.EzCentering[0], tv.nbrCells[0]),
layout.allocSizeDerived(interpOrder, tv.EzCentering[1],
tv.nbrCells[1])
],
dtype=np.float64)
nbrGhost_p = layout.nbrGhosts(interpOrder, 'primal')
nbrGhost_d = layout.nbrGhosts(interpOrder, 'dual')
x_dual = tv.meshSize[0] * np.arange(
layout.allocSize(interpOrder, 'dual', tv.nbrCells[0])
) - tv.meshSize[0] * nbrGhost_d + tv.meshSize[0] * 0.5
y_dual = tv.meshSize[1] * np.arange(
layout.allocSize(interpOrder, 'dual', tv.nbrCells[1])
) - tv.meshSize[1] * nbrGhost_d + tv.meshSize[1] * 0.5
x_primal = tv.meshSize[0] * np.arange(
layout.allocSize(interpOrder, 'primal',
tv.nbrCells[0])) - tv.meshSize[0] * nbrGhost_p
y_primal = tv.meshSize[1] * np.arange(
layout.allocSize(interpOrder, 'primal',
tv.nbrCells[1])) - tv.meshSize[1] * nbrGhost_p
By = np.tensordot(np.cos(2 * np.pi / tv.domainSize[0] * x_dual),
np.sin(2 * np.pi / tv.domainSize[1] * y_primal),
axes=0)
Ez = np.tensordot(np.cos(2 * np.pi / tv.domainSize[0] * x_primal),
np.sin(2 * np.pi / tv.domainSize[1] * y_primal),
axes=0)
psi_d_X = layout.physicalStartIndex(interpOrder, 'dual')
pei_d_X = layout.physicalEndIndex(interpOrder, 'dual', tv.nbrCells[0])
psi_d_Y = layout.physicalStartIndex(interpOrder, 'dual')
pei_d_Y = layout.physicalEndIndex(interpOrder, 'dual', tv.nbrCells[1])
psi_p_X = layout.physicalStartIndex(interpOrder, 'primal')
pei_p_X = layout.physicalEndIndex(interpOrder, 'primal',
tv.nbrCells[0])
psi_p_Y = layout.physicalStartIndex(interpOrder, 'primal')
pei_p_Y = layout.physicalEndIndex(interpOrder, 'primal',
tv.nbrCells[1])
dxBy[psi_p_X:pei_p_X +
1, :] = (By[psi_d_X:pei_d_X + 2, :] -
By[psi_d_X - 1:pei_d_X + 1, :]) / tv.meshSize[0]
dxEz[psi_d_X:pei_d_X +
1, :] = (Ez[psi_p_X + 1:pei_p_X + 1, :] -
Ez[psi_p_X:pei_p_X, :]) / tv.meshSize[0]
dyBy[:,
psi_d_Y:pei_d_Y + 1] = (By[:, psi_p_Y + 1:pei_p_Y + 1] -
By[:, psi_p_Y:pei_p_Y]) / tv.meshSize[1]
dyEz[:,
psi_d_Y:pei_d_Y + 1] = (Ez[:, psi_p_Y + 1:pei_p_Y + 1] -
Ez[:, psi_p_Y:pei_p_Y]) / tv.meshSize[1]
np.savetxt(os.path.join(path, filename_dxBy),
dxBy.flatten('C'),
delimiter=" ")
np.savetxt(os.path.join(path, filename_dyBy),
dyBy.flatten('C'),
delimiter=" ")
np.savetxt(os.path.join(path, filename_dxEz),
dxEz.flatten('C'),
delimiter=" ")
np.savetxt(os.path.join(path, filename_dyEz),
dyEz.flatten('C'),
delimiter=" ")
def test_ohm_yee3D(path):
layout = gridlayout.GridLayout() # yee layout
tv = TestVariables()
eta = 1.0
nu = 0.001
Vx = np.zeros([
layout.allocSize(tv.interpOrder, tv.MomentsCentering[0],
tv.nbrCells[0]),
layout.allocSize(tv.interpOrder, tv.MomentsCentering[1],
tv.nbrCells[1]),
layout.allocSize(tv.interpOrder, tv.MomentsCentering[2],
tv.nbrCells[2])
],
dtype=np.float64)
Vy = np.zeros([
layout.allocSize(tv.interpOrder, tv.MomentsCentering[0],
tv.nbrCells[0]),
layout.allocSize(tv.interpOrder, tv.MomentsCentering[1],
tv.nbrCells[1]),
layout.allocSize(tv.interpOrder, tv.MomentsCentering[2],
tv.nbrCells[2])
],
dtype=np.float64)
Vz = np.zeros([
layout.allocSize(tv.interpOrder, tv.MomentsCentering[0],
tv.nbrCells[0]),
layout.allocSize(tv.interpOrder, tv.MomentsCentering[1],
tv.nbrCells[1]),
layout.allocSize(tv.interpOrder, tv.MomentsCentering[2],
tv.nbrCells[2])
],
dtype=np.float64)
Bx = np.zeros([
layout.allocSize(tv.interpOrder, tv.BxCentering[0], tv.nbrCells[0]),
layout.allocSize(tv.interpOrder, tv.BxCentering[1], tv.nbrCells[1]),
layout.allocSize(tv.interpOrder, tv.BxCentering[2], tv.nbrCells[2])
],
dtype=np.float64)
By = np.zeros([
layout.allocSize(tv.interpOrder, tv.ByCentering[0], tv.nbrCells[0]),
layout.allocSize(tv.interpOrder, tv.ByCentering[1], tv.nbrCells[1]),
layout.allocSize(tv.interpOrder, tv.ByCentering[2], tv.nbrCells[2])
],
dtype=np.float64)
Bz = np.zeros([
layout.allocSize(tv.interpOrder, tv.BzCentering[0], tv.nbrCells[0]),
layout.allocSize(tv.interpOrder, tv.BzCentering[1], tv.nbrCells[1]),
layout.allocSize(tv.interpOrder, tv.BzCentering[2], tv.nbrCells[2])
],
dtype=np.float64)
n = np.zeros([
layout.allocSize(tv.interpOrder, tv.MomentsCentering[0],
tv.nbrCells[0]),
layout.allocSize(tv.interpOrder, tv.MomentsCentering[1],
tv.nbrCells[1]),
layout.allocSize(tv.interpOrder, tv.MomentsCentering[2],
tv.nbrCells[2])
],
dtype=np.float64)
P = np.zeros([
layout.allocSize(tv.interpOrder, tv.MomentsCentering[0],
tv.nbrCells[0]),
layout.allocSize(tv.interpOrder, tv.MomentsCentering[1],
tv.nbrCells[1]),
layout.allocSize(tv.interpOrder, tv.MomentsCentering[2],
tv.nbrCells[2])
],
dtype=np.float64)
Jx = np.zeros([
layout.allocSize(tv.interpOrder, tv.JxCentering[0], tv.nbrCells[0]),
layout.allocSize(tv.interpOrder, tv.JxCentering[1], tv.nbrCells[1]),
layout.allocSize(tv.interpOrder, tv.JxCentering[2], tv.nbrCells[2])
],
dtype=np.float64)
Jy = np.zeros([
layout.allocSize(tv.interpOrder, tv.JyCentering[0], tv.nbrCells[0]),
layout.allocSize(tv.interpOrder, tv.JyCentering[1], tv.nbrCells[1]),
layout.allocSize(tv.interpOrder, tv.JyCentering[2], tv.nbrCells[2])
],
dtype=np.float64)
Jz = np.zeros([
layout.allocSize(tv.interpOrder, tv.JzCentering[0], tv.nbrCells[0]),
layout.allocSize(tv.interpOrder, tv.JzCentering[1], tv.nbrCells[1]),
layout.allocSize(tv.interpOrder, tv.JzCentering[2], tv.nbrCells[2])
],
dtype=np.float64)
idealx = np.zeros([
layout.allocSize(tv.interpOrder, tv.ExCentering[0], tv.nbrCells[0]),
layout.allocSize(tv.interpOrder, tv.ExCentering[1], tv.nbrCells[1]),
layout.allocSize(tv.interpOrder, tv.ExCentering[2], tv.nbrCells[2])
],
dtype=np.float64)
idealy = np.zeros([
layout.allocSize(tv.interpOrder, tv.EyCentering[0], tv.nbrCells[0]),
layout.allocSize(tv.interpOrder, tv.EyCentering[1], tv.nbrCells[1]),
layout.allocSize(tv.interpOrder, tv.EyCentering[2], tv.nbrCells[2])
],
dtype=np.float64)
idealz = np.zeros([
layout.allocSize(tv.interpOrder, tv.EzCentering[0], tv.nbrCells[0]),
layout.allocSize(tv.interpOrder, tv.EzCentering[1], tv.nbrCells[1]),
layout.allocSize(tv.interpOrder, tv.EzCentering[2], tv.nbrCells[2])
],
dtype=np.float64)
pressx = np.zeros([
layout.allocSize(tv.interpOrder, tv.ExCentering[0], tv.nbrCells[0]),
layout.allocSize(tv.interpOrder, tv.ExCentering[1], tv.nbrCells[1]),
layout.allocSize(tv.interpOrder, tv.ExCentering[2], tv.nbrCells[2])
],
dtype=np.float64)
pressy = np.zeros([
layout.allocSize(tv.interpOrder, tv.EyCentering[0], tv.nbrCells[0]),
layout.allocSize(tv.interpOrder, tv.EyCentering[1], tv.nbrCells[1]),
layout.allocSize(tv.interpOrder, tv.EyCentering[2], tv.nbrCells[2])
],
dtype=np.float64)
pressz = np.zeros([
layout.allocSize(tv.interpOrder, tv.EzCentering[0], tv.nbrCells[0]),
layout.allocSize(tv.interpOrder, tv.EzCentering[1], tv.nbrCells[1]),
layout.allocSize(tv.interpOrder, tv.EzCentering[2], tv.nbrCells[2])
],
dtype=np.float64)
resistx = np.zeros([
layout.allocSize(tv.interpOrder, tv.ExCentering[0], tv.nbrCells[0]),
layout.allocSize(tv.interpOrder, tv.ExCentering[1], tv.nbrCells[1]),
layout.allocSize(tv.interpOrder, tv.ExCentering[2], tv.nbrCells[2])
],
dtype=np.float64)
resisty = np.zeros([
layout.allocSize(tv.interpOrder, tv.EyCentering[0], tv.nbrCells[0]),
layout.allocSize(tv.interpOrder, tv.EyCentering[1], tv.nbrCells[1]),
layout.allocSize(tv.interpOrder, tv.EyCentering[2], tv.nbrCells[2])
],
dtype=np.float64)
resistz = np.zeros([
layout.allocSize(tv.interpOrder, tv.EzCentering[0], tv.nbrCells[0]),
layout.allocSize(tv.interpOrder, tv.EzCentering[1], tv.nbrCells[1]),
layout.allocSize(tv.interpOrder, tv.EzCentering[2], tv.nbrCells[2])
],
dtype=np.float64)
viscousx = np.zeros([
layout.allocSize(tv.interpOrder, tv.ExCentering[0], tv.nbrCells[0]),
layout.allocSize(tv.interpOrder, tv.ExCentering[1], tv.nbrCells[1]),
layout.allocSize(tv.interpOrder, tv.ExCentering[2], tv.nbrCells[2])
],
dtype=np.float64)
viscousy = np.zeros([
layout.allocSize(tv.interpOrder, tv.EyCentering[0], tv.nbrCells[0]),
layout.allocSize(tv.interpOrder, tv.EyCentering[1], tv.nbrCells[1]),
layout.allocSize(tv.interpOrder, tv.EyCentering[2], tv.nbrCells[2])
],
dtype=np.float64)
viscousz = np.zeros([
layout.allocSize(tv.interpOrder, tv.EzCentering[0], tv.nbrCells[0]),
layout.allocSize(tv.interpOrder, tv.EzCentering[1], tv.nbrCells[1]),
layout.allocSize(tv.interpOrder, tv.EzCentering[2], tv.nbrCells[2])
],
dtype=np.float64)
ExNew = np.zeros([
layout.allocSize(tv.interpOrder, tv.ExCentering[0], tv.nbrCells[0]),
layout.allocSize(tv.interpOrder, tv.ExCentering[1], tv.nbrCells[1]),
layout.allocSize(tv.interpOrder, tv.ExCentering[2], tv.nbrCells[2])
],
dtype=np.float64)
EyNew = np.zeros([
layout.allocSize(tv.interpOrder, tv.EyCentering[0], tv.nbrCells[0]),
layout.allocSize(tv.interpOrder, tv.EyCentering[1], tv.nbrCells[1]),
layout.allocSize(tv.interpOrder, tv.EyCentering[2], tv.nbrCells[2])
],
dtype=np.float64)
EzNew = np.zeros([
layout.allocSize(tv.interpOrder, tv.EzCentering[0], tv.nbrCells[0]),
layout.allocSize(tv.interpOrder, tv.EzCentering[1], tv.nbrCells[1]),
layout.allocSize(tv.interpOrder, tv.EzCentering[2], tv.nbrCells[2])
],
dtype=np.float64)
psi_p_X = layout.physicalStartIndex(tv.interpOrder, 'primal')
pei_p_X = layout.physicalEndIndex(tv.interpOrder, 'primal', tv.nbrCells[0])
psi_p_Y = layout.physicalStartIndex(tv.interpOrder, 'primal')
pei_p_Y = layout.physicalEndIndex(tv.interpOrder, 'primal', tv.nbrCells[1])
psi_p_Z = layout.physicalStartIndex(tv.interpOrder, 'primal')
pei_p_Z = layout.physicalEndIndex(tv.interpOrder, 'primal', tv.nbrCells[2])
psi_d_X = layout.physicalStartIndex(tv.interpOrder, 'dual')
pei_d_X = layout.physicalEndIndex(tv.interpOrder, 'dual', tv.nbrCells[0])
psi_d_Y = layout.physicalStartIndex(tv.interpOrder, 'dual')
pei_d_Y = layout.physicalEndIndex(tv.interpOrder, 'dual', tv.nbrCells[1])
psi_d_Z = layout.physicalStartIndex(tv.interpOrder, 'dual')
pei_d_Z = layout.physicalEndIndex(tv.interpOrder, 'dual', tv.nbrCells[2])
nbrGhost_p = layout.nbrGhosts(tv.interpOrder, 'primal')
nbrGhost_d = layout.nbrGhosts(tv.interpOrder, 'dual')
x_primal = tv.meshSize[0] * np.arange(
layout.allocSize(tv.interpOrder, 'primal',
tv.nbrCells[0])) - tv.meshSize[0] * nbrGhost_p
y_primal = tv.meshSize[1] * np.arange(
layout.allocSize(tv.interpOrder, 'primal',
tv.nbrCells[1])) - tv.meshSize[1] * nbrGhost_p
z_primal = tv.meshSize[2] * np.arange(
layout.allocSize(tv.interpOrder, 'primal',
tv.nbrCells[2])) - tv.meshSize[2] * nbrGhost_p
x_dual = tv.meshSize[0] * np.arange(
layout.allocSize(tv.interpOrder, 'dual', tv.nbrCells[0])
) - tv.meshSize[0] * nbrGhost_d + tv.meshSize[0] * 0.5
y_dual = tv.meshSize[1] * np.arange(
layout.allocSize(tv.interpOrder, 'dual', tv.nbrCells[1])
) - tv.meshSize[1] * nbrGhost_d + tv.meshSize[1] * 0.5
z_dual = tv.meshSize[2] * np.arange(
layout.allocSize(tv.interpOrder, 'dual', tv.nbrCells[2])
) - tv.meshSize[2] * nbrGhost_d + tv.meshSize[2] * 0.5
# analytical profiles of density, velocity...
Vx = np.tensordot(np.cosh(0.2 * x_primal),
np.tensordot(np.sinh(0.2 * y_primal),
np.tanh(0.2 * z_primal),
axes=0),
axes=0)
Vy = np.tensordot(np.cosh(0.4 * x_primal),
np.tensordot(np.sinh(0.4 * y_primal),
np.tanh(0.4 * z_primal),
axes=0),
axes=0)
Vz = np.tensordot(np.cosh(0.3 * x_primal),
np.tensordot(np.sinh(0.3 * y_primal),
np.tanh(0.3 * z_primal),
axes=0),
axes=0)
Bx = np.tensordot(np.tanh(0.2 * x_primal),
np.tensordot(np.sinh(0.2 * y_dual),
np.cosh(0.2 * z_dual),
axes=0),
axes=0)
By = np.tensordot(np.tanh(0.4 * x_dual),
np.tensordot(np.sinh(0.4 * y_primal),
np.cosh(0.4 * z_dual),
axes=0),
axes=0)
Bz = np.tensordot(np.tanh(0.3 * x_dual),
np.tensordot(np.sinh(0.3 * y_dual),
np.cosh(0.3 * z_primal),
axes=0),
axes=0)
n = np.tensordot(np.exp(-0.1 * x_primal),
np.tensordot(np.exp(-0.1 * y_primal),
np.exp(-0.1 * z_primal),
axes=0),
axes=0)
P = np.tensordot(np.exp(-0.2 * x_primal),
np.tensordot(np.exp(-0.2 * y_primal),
np.exp(-0.2 * z_primal),
axes=0),
axes=0)
Jx = np.tensordot(np.sinh(0.1 * x_dual),
np.tensordot(np.sinh(0.1 * y_primal),
np.tanh(0.1 * z_primal),
axes=0),
axes=0)
Jy = np.tensordot(np.sinh(0.3 * x_primal),
np.tensordot(np.sinh(0.3 * y_dual),
np.tanh(0.3 * z_primal),
axes=0),
axes=0)
Jz = np.tensordot(np.sinh(0.2 * x_primal),
np.tensordot(np.sinh(0.2 * y_primal),
np.tanh(0.2 * z_dual),
axes=0),
axes=0)
# ideal term
idealx[psi_d_X :pei_d_X+1, psi_p_Y :pei_p_Y+1, psi_p_Z :pei_p_Z+1] = \
-0.25*(Vy[psi_p_X :pei_p_X , psi_p_Y :pei_p_Y+1, psi_p_Z :pei_p_Z+1]\
+Vy[psi_p_X+1:pei_p_X+1, psi_p_Y :pei_p_Y+1, psi_p_Z :pei_p_Z+1])\
*(Bz[psi_d_X :pei_d_X+1, psi_d_Y-1:pei_d_Y+1, psi_p_Z :pei_p_Z+1]\
+Bz[psi_d_X :pei_d_X+1, psi_d_Y :pei_d_Y+2, psi_p_Z :pei_p_Z+1])\
+0.25*(Vz[psi_p_X :pei_p_X , psi_p_Y :pei_p_Y+1, psi_p_Z :pei_p_Z+1]\
+Vz[psi_p_X+1:pei_p_X+1, psi_p_Y :pei_p_Y+1, psi_p_Z :pei_p_Z+1])\
*(By[psi_d_X :pei_d_X+1, psi_p_Y :pei_p_Y+1, psi_d_Z-1:pei_d_Z+1]\
+By[psi_d_X :pei_d_X+1, psi_p_Y :pei_p_Y+1, psi_d_Z :pei_d_Z+2])
idealy[psi_p_X :pei_p_X+1, psi_d_Y :pei_d_Y+1, psi_p_Z :pei_p_Z+1] = \
-0.25*(Vz[psi_p_X :pei_p_X+1, psi_p_Y :pei_p_Y , psi_p_Z :pei_p_Z+1]\
+Vz[psi_p_X :pei_p_X+1, psi_p_Y+1:pei_p_Y+1, psi_p_Z :pei_p_Z+1])\
*(Bx[psi_p_X :pei_p_X+1, psi_d_Y :pei_d_Y+1, psi_d_Z-1:pei_d_Z+1]\
+Bx[psi_p_X :pei_p_X+1, psi_d_Y :pei_d_Y+1, psi_d_Z :pei_d_Z+2])\
+0.25*(Vx[psi_p_X :pei_p_X+1, psi_p_Y :pei_p_Y , psi_p_Z :pei_p_Z+1]\
+Vx[psi_p_X :pei_p_X+1, psi_p_Y+1:pei_p_Y+1, psi_p_Z :pei_p_Z+1])\
*(Bz[psi_d_X-1:pei_d_X+1, psi_d_Y :pei_d_Y+1, psi_p_Z :pei_p_Z+1]\
+Bz[psi_d_X :pei_d_X+2, psi_d_Y :pei_d_Y+1, psi_p_Z :pei_p_Z+1])
idealz[psi_p_X :pei_p_X+1, psi_p_Y :pei_p_Y+1, psi_d_Z :pei_d_Z+1] = \
-0.25*(Vx[psi_p_X :pei_p_X+1, psi_p_Y :pei_p_Y+1, psi_p_Z :pei_p_Z ]\
+Vx[psi_p_X :pei_p_X+1, psi_p_Y :pei_p_Y+1, psi_p_Z+1:pei_p_Z+1])\
*(By[psi_d_X-1:pei_d_X+1, psi_p_Y :pei_p_Y+1, psi_d_Z :pei_d_Z+1]\
+By[psi_d_X :pei_d_X+2, psi_p_Y :pei_p_Y+1, psi_d_Z :pei_d_Z+1])\
+0.25*(Vy[psi_p_X :pei_p_X+1, psi_p_Y :pei_p_Y+1, psi_p_Z :pei_p_Z ]\
+Vy[psi_p_X :pei_p_X+1, psi_p_Y :pei_p_Y+1, psi_p_Z+1:pei_p_Z+1])\
*(Bx[psi_p_X :pei_p_X+1, psi_d_Y-1:pei_d_Y+1, psi_d_Z :pei_d_Z+1]\
+Bx[psi_p_X :pei_p_X+1, psi_d_Y :pei_d_Y+2, psi_d_Z :pei_d_Z+1])
# pressure term
pressx[psi_d_X :pei_d_X+1, psi_p_Y :pei_p_Y+1, psi_p_Z :pei_p_Z+1] = \
((P[psi_p_X+1:pei_p_X+1, psi_p_Y :pei_p_Y+1, psi_p_Z :pei_p_Z+1]\
-P[psi_p_X :pei_p_X , psi_p_Y :pei_p_Y+1, psi_p_Z :pei_p_Z+1])/tv.meshSize[0])\
/(0.5*(n[psi_p_X :pei_p_X , psi_p_Y :pei_p_Y+1, psi_p_Z :pei_p_Z+1]\
+n[psi_p_X+1:pei_p_X+1, psi_p_Y :pei_p_Y+1, psi_p_Z :pei_p_Z+1]))
pressy[psi_p_X :pei_p_X+1, psi_d_Y :pei_d_Y+1, psi_p_Z :pei_p_Z+1] = \
((P[psi_p_X :pei_p_X+1, psi_p_Y+1:pei_p_Y+1, psi_p_Z :pei_p_Z+1]\
-P[psi_p_X :pei_p_X+1, psi_p_Y :pei_p_Y , psi_p_Z :pei_p_Z+1])/tv.meshSize[1])\
/(0.5*(n[psi_p_X :pei_p_X+1, psi_p_Y :pei_p_Y , psi_p_Z :pei_p_Z+1]\
+n[psi_p_X :pei_p_X+1, psi_p_Y+1:pei_p_Y+1, psi_p_Z :pei_p_Z+1]))
pressz[psi_p_X :pei_p_X+1, psi_p_Y :pei_p_Y+1, psi_d_Z :pei_d_Z+1] = \
((P[psi_p_X :pei_p_X+1, psi_p_Y :pei_p_Y+1, psi_p_Z+1:pei_p_Z+1]\
-P[psi_p_X :pei_p_X+1, psi_p_Y :pei_p_Y+1, psi_p_Z :pei_p_Z ])/tv.meshSize[2])\
/(0.5*(n[psi_p_X :pei_p_X+1, psi_p_Y :pei_p_Y+1, psi_p_Z :pei_p_Z ]\
+n[psi_p_X :pei_p_X+1, psi_p_Y :pei_p_Y+1, psi_p_Z+1:pei_p_Z+1]))
# resistive term
resistx[psi_d_X:pei_d_X+1, psi_p_Y:pei_p_Y+1, psi_p_Z :pei_p_Z+1] = \
eta*Jx[psi_d_X:pei_d_X+1, psi_p_Y:pei_p_Y+1, psi_p_Z :pei_p_Z+1]
resisty[psi_p_X:pei_p_X+1, psi_d_Y:pei_d_Y+1, psi_p_Z :pei_p_Z+1] = \
eta*Jy[psi_p_X:pei_p_X+1, psi_d_Y:pei_d_Y+1, psi_p_Z :pei_p_Z+1]
resistz[psi_p_X:pei_p_X+1, psi_p_Y:pei_p_Y+1, psi_d_Z :pei_d_Z+1] = \
eta*Jz[psi_p_X:pei_p_X+1, psi_p_Y:pei_p_Y+1, psi_d_Z :pei_d_Z+1]
# viscous term
viscousx[psi_d_X :pei_d_X+1, psi_p_Y :pei_p_Y+1, psi_p_Z :pei_p_Z+1] = \
-nu*(Jx[psi_d_X-1:pei_d_X , psi_p_Y :pei_p_Y+1, psi_p_Z :pei_p_Z+1]\
-2.0*Jx[psi_d_X :pei_d_X+1, psi_p_Y :pei_p_Y+1, psi_p_Z :pei_p_Z+1]\
+Jx[psi_d_X+1:pei_d_X+2, psi_p_Y :pei_p_Y+1, psi_p_Z :pei_p_Z+1])\
/(tv.meshSize[0]*tv.meshSize[0])\
-nu*(Jx[psi_d_X :pei_d_X+1, psi_p_Y-1:pei_p_Y , psi_p_Z :pei_p_Z+1]\
-2.0*Jx[psi_d_X :pei_d_X+1, psi_p_Y :pei_p_Y+1, psi_p_Z :pei_p_Z+1]\
+Jx[psi_d_X :pei_d_X+1, psi_p_Y+1:pei_p_Y+2, psi_p_Z :pei_p_Z+1])\
/(tv.meshSize[1]*tv.meshSize[1])\
-nu*(Jx[psi_d_X :pei_d_X+1, psi_p_Y :pei_p_Y+1, psi_p_Z-1:pei_p_Z ]\
-2.0*Jx[psi_d_X :pei_d_X+1, psi_p_Y :pei_p_Y+1, psi_p_Z :pei_p_Z+1]\
+Jx[psi_d_X :pei_d_X+1, psi_p_Y :pei_p_Y+1, psi_p_Z+1:pei_p_Z+2])\
/(tv.meshSize[2]*tv.meshSize[2])
viscousy[psi_p_X :pei_p_X+1, psi_d_Y :pei_d_Y+1, psi_p_Z :pei_p_Z+1] = \
-nu*(Jy[psi_p_X-1:pei_p_X , psi_d_Y :pei_d_Y+1, psi_p_Z :pei_p_Z+1]\
-2.0*Jy[psi_p_X :pei_p_X+1, psi_d_Y :pei_d_Y+1, psi_p_Z :pei_p_Z+1]\
+Jy[psi_p_X+1:pei_p_X+2, psi_d_Y :pei_d_Y+1, psi_p_Z :pei_p_Z+1])\
/(tv.meshSize[0]*tv.meshSize[0])\
-nu*(Jy[psi_p_X :pei_p_X+1, psi_d_Y-1:pei_d_Y , psi_p_Z :pei_p_Z+1]\
-2.0*Jy[psi_p_X :pei_p_X+1, psi_d_Y :pei_d_Y+1, psi_p_Z :pei_p_Z+1]\
+Jy[psi_p_X :pei_p_X+1, psi_d_Y+1:pei_d_Y+2, psi_p_Z :pei_p_Z+1])\
/(tv.meshSize[1]*tv.meshSize[1])\
-nu*(Jy[psi_p_X :pei_p_X+1, psi_d_Y :pei_d_Y+1, psi_p_Z-1:pei_p_Z ]\
-2.0*Jy[psi_p_X :pei_p_X+1, psi_d_Y :pei_d_Y+1, psi_p_Z :pei_p_Z+1]\
+Jy[psi_p_X :pei_p_X+1, psi_d_Y :pei_d_Y+1, psi_p_Z+1:pei_p_Z+2])\
/(tv.meshSize[2]*tv.meshSize[2])
viscousz[psi_p_X :pei_p_X+1, psi_p_Y :pei_p_Y+1, psi_d_Z :pei_d_Z+1] = \
-nu*(Jz[psi_p_X-1:pei_p_X , psi_p_Y :pei_p_Y+1, psi_d_Z :pei_d_Z+1]\
-2.0*Jz[psi_p_X :pei_p_X+1, psi_p_Y :pei_p_Y+1, psi_d_Z :pei_d_Z+1]\
+Jz[psi_p_X+1:pei_p_X+2, psi_p_Y :pei_p_Y+1, psi_d_Z :pei_d_Z+1])\
/(tv.meshSize[0]*tv.meshSize[0])\
-nu*(Jz[psi_p_X :pei_p_X+1, psi_p_Y-1:pei_p_Y , psi_d_Z :pei_d_Z+1]\
-2.0*Jz[psi_p_X :pei_p_X+1, psi_p_Y :pei_p_Y+1, psi_d_Z :pei_d_Z+1]\
+Jz[psi_p_X :pei_p_X+1, psi_p_Y+1:pei_p_Y+2, psi_d_Z :pei_d_Z+1])\
/(tv.meshSize[1]*tv.meshSize[1])\
-nu*(Jz[psi_p_X :pei_p_X+1, psi_p_Y :pei_p_Y+1, psi_d_Z-1:pei_d_Z ]\
-2.0*Jz[psi_p_X :pei_p_X+1, psi_p_Y :pei_p_Y+1, psi_d_Z :pei_d_Z+1]\
+Jz[psi_p_X :pei_p_X+1, psi_p_Y :pei_p_Y+1, psi_d_Z+1:pei_d_Z+2])\
/(tv.meshSize[2]*tv.meshSize[2])
ExNew = idealx + pressx + resistx + viscousx
EyNew = idealy + pressy + resisty + viscousy
EzNew = idealz + pressz + resistz + viscousz
filename_ohmx = "ohmx_yee_3D_order1.txt"
filename_ohmy = "ohmy_yee_3D_order1.txt"
filename_ohmz = "ohmz_yee_3D_order1.txt"
np.savetxt(os.path.join(path, filename_ohmx),
ExNew.flatten('C'),
delimiter=" ")
np.savetxt(os.path.join(path, filename_ohmy),
EyNew.flatten('C'),
delimiter=" ")
np.savetxt(os.path.join(path, filename_ohmz),
EzNew.flatten('C'),
delimiter=" ")
def test_ohm_yee1D(path):
layout = gridlayout.GridLayout() # yee layout
tv = TestVariables()
eta = 1.0
nu = 0.001
Vx = np.zeros(layout.allocSize(tv.interpOrder, tv.MomentsCentering[0],
tv.nbrCells[0]),
dtype=np.float64)
Vy = np.zeros(layout.allocSize(tv.interpOrder, tv.MomentsCentering[0],
tv.nbrCells[0]),
dtype=np.float64)
Vz = np.zeros(layout.allocSize(tv.interpOrder, tv.MomentsCentering[0],
tv.nbrCells[0]),
dtype=np.float64)
Bx = np.zeros(layout.allocSize(tv.interpOrder, tv.BxCentering[0],
tv.nbrCells[0]),
dtype=np.float64)
By = np.zeros(layout.allocSize(tv.interpOrder, tv.ByCentering[0],
tv.nbrCells[0]),
dtype=np.float64)
Bz = np.zeros(layout.allocSize(tv.interpOrder, tv.BzCentering[0],
tv.nbrCells[0]),
dtype=np.float64)
n = np.zeros(layout.allocSize(tv.interpOrder, tv.MomentsCentering[0],
tv.nbrCells[0]),
dtype=np.float64)
P = np.zeros(layout.allocSize(tv.interpOrder, tv.MomentsCentering[0],
tv.nbrCells[0]),
dtype=np.float64)
Jx = np.zeros(layout.allocSize(tv.interpOrder, tv.JxCentering[0],
tv.nbrCells[0]),
dtype=np.float64)
Jy = np.zeros(layout.allocSize(tv.interpOrder, tv.JyCentering[0],
tv.nbrCells[0]),
dtype=np.float64)
Jz = np.zeros(layout.allocSize(tv.interpOrder, tv.JzCentering[0],
tv.nbrCells[0]),
dtype=np.float64)
idealx = np.zeros(layout.allocSize(tv.interpOrder, tv.ExCentering[0],
tv.nbrCells[0]),
dtype=np.float64)
idealy = np.zeros(layout.allocSize(tv.interpOrder, tv.EyCentering[0],
tv.nbrCells[0]),
dtype=np.float64)
idealz = np.zeros(layout.allocSize(tv.interpOrder, tv.EzCentering[0],
tv.nbrCells[0]),
dtype=np.float64)
pressx = np.zeros(layout.allocSize(tv.interpOrder, tv.ExCentering[0],
tv.nbrCells[0]),
dtype=np.float64)
pressy = np.zeros(layout.allocSize(tv.interpOrder, tv.EyCentering[0],
tv.nbrCells[0]),
dtype=np.float64)
pressz = np.zeros(layout.allocSize(tv.interpOrder, tv.EzCentering[0],
tv.nbrCells[0]),
dtype=np.float64)
resistx = np.zeros(layout.allocSize(tv.interpOrder, tv.ExCentering[0],
tv.nbrCells[0]),
dtype=np.float64)
resisty = np.zeros(layout.allocSize(tv.interpOrder, tv.EyCentering[0],
tv.nbrCells[0]),
dtype=np.float64)
resistz = np.zeros(layout.allocSize(tv.interpOrder, tv.EzCentering[0],
tv.nbrCells[0]),
dtype=np.float64)
viscousx = np.zeros(layout.allocSize(tv.interpOrder, tv.ExCentering[0],
tv.nbrCells[0]),
dtype=np.float64)
viscousy = np.zeros(layout.allocSize(tv.interpOrder, tv.EyCentering[0],
tv.nbrCells[0]),
dtype=np.float64)
viscousz = np.zeros(layout.allocSize(tv.interpOrder, tv.EzCentering[0],
tv.nbrCells[0]),
dtype=np.float64)
ExNew = np.zeros(layout.allocSize(tv.interpOrder, tv.ExCentering[0],
tv.nbrCells[0]),
dtype=np.float64)
EyNew = np.zeros(layout.allocSize(tv.interpOrder, tv.EyCentering[0],
tv.nbrCells[0]),
dtype=np.float64)
EzNew = np.zeros(layout.allocSize(tv.interpOrder, tv.EzCentering[0],
tv.nbrCells[0]),
dtype=np.float64)
psi_p_X = layout.physicalStartIndex(tv.interpOrder, 'primal')
pei_p_X = layout.physicalEndIndex(tv.interpOrder, 'primal', tv.nbrCells[0])
psi_d_X = layout.physicalStartIndex(tv.interpOrder, 'dual')
pei_d_X = layout.physicalEndIndex(tv.interpOrder, 'dual', tv.nbrCells[0])
nbrGhost_p = layout.nbrGhosts(tv.interpOrder, 'primal')
nbrGhost_d = layout.nbrGhosts(tv.interpOrder, 'dual')
x_primal = tv.meshSize[0] * np.arange(
layout.allocSize(tv.interpOrder, 'primal',
tv.nbrCells[0])) - tv.meshSize[0] * nbrGhost_p
x_dual = tv.meshSize[0] * np.arange(
layout.allocSize(tv.interpOrder, 'dual', tv.nbrCells[0])
) - tv.meshSize[0] * nbrGhost_d + tv.meshSize[0] * 0.5
# analytical profiles ov density, velocity...
Vx = np.cosh(0.2 * x_primal)
Vy = np.cosh(0.4 * x_primal)
Vz = np.cosh(0.3 * x_primal)
Bx = np.tanh(0.2 * x_primal)
By = np.tanh(3.0 * x_dual)
Bz = np.tanh(1.2 * x_dual)
n = np.sinh(0.5 * x_primal)
P = np.sinh(0.8 * x_primal)
Jx = np.sinh(0.1 * x_dual)
Jy = np.sinh(0.3 * x_primal)
Jz = np.sinh(0.2 * x_primal)
# ideal term
idealx[psi_d_X:pei_d_X+1] = 0.5*(Vz[psi_p_X:pei_p_X]+Vz[psi_p_X+1:pei_p_X+1])*By[psi_d_X:pei_d_X+1]\
- 0.5*(Vy[psi_p_X:pei_p_X]+Vy[psi_p_X+1:pei_p_X+1])*Bz[psi_d_X:pei_d_X+1]
idealy[psi_p_X:pei_p_X+1] = 0.5*Vx[psi_p_X:pei_p_X+1]*(Bz[psi_d_X-1:pei_d_X+1]+Bz[psi_d_X:pei_d_X+2])\
- Vz[psi_p_X:pei_p_X+1]*Bx[psi_p_X:pei_p_X+1]
idealz[psi_p_X:pei_p_X+1] = Vy[psi_p_X:pei_p_X+1]*Bx[psi_p_X:pei_p_X+1]\
- 0.5*Vx[psi_p_X:pei_p_X+1]*(By[psi_d_X-1:pei_d_X+1]+By[psi_d_X:pei_d_X+2])
# pressure term
pressx[psi_d_X:pei_d_X+1] = ((P[psi_p_X+1:pei_p_X+1]-P[psi_p_X:pei_p_X])/tv.meshSize[0])\
/(0.5*(n[psi_p_X:pei_p_X]+n[psi_p_X+1:pei_p_X+1]))
pressy[psi_p_X:pei_p_X + 1] = 0
pressz[psi_p_X:pei_p_X + 1] = 0
# resistive term
resistx[psi_d_X:pei_d_X + 1] = eta * Jx[psi_d_X:pei_d_X + 1]
resisty[psi_p_X:pei_p_X + 1] = eta * Jy[psi_p_X:pei_p_X + 1]
resistz[psi_p_X:pei_p_X + 1] = eta * Jz[psi_p_X:pei_p_X + 1]
# viscous term
viscousx[psi_d_X:pei_d_X + 1] = -nu * (
Jx[psi_d_X - 1:pei_d_X] - 2.0 * Jx[psi_d_X:pei_d_X + 1] +
Jx[psi_d_X + 1:pei_d_X + 2]) / (tv.meshSize[0] * tv.meshSize[0])
viscousy[psi_p_X:pei_p_X + 1] = -nu * (
Jy[psi_p_X - 1:pei_p_X] - 2.0 * Jy[psi_p_X:pei_p_X + 1] +
Jy[psi_p_X + 1:pei_p_X + 2]) / (tv.meshSize[0] * tv.meshSize[0])
viscousz[psi_p_X:pei_p_X + 1] = -nu * (
Jz[psi_p_X - 1:pei_p_X] - 2.0 * Jz[psi_p_X:pei_p_X + 1] +
Jz[psi_p_X + 1:pei_p_X + 2]) / (tv.meshSize[0] * tv.meshSize[0])
ExNew = idealx + pressx + resistx + viscousx
EyNew = idealy + pressy + resisty + viscousy
EzNew = idealz + pressz + resistz + viscousz
filename_ohmx = "ohmx_yee_1D_order1.txt"
filename_ohmy = "ohmy_yee_1D_order1.txt"
filename_ohmz = "ohmz_yee_1D_order1.txt"
np.savetxt(os.path.join(path, filename_ohmx), ExNew, delimiter=" ")
np.savetxt(os.path.join(path, filename_ohmy), EyNew, delimiter=" ")
np.savetxt(os.path.join(path, filename_ohmz), EzNew, delimiter=" ")
def test_ampere_yee2D(path):
layout = gridlayout.GridLayout() # yee layout
tv = TestVariables()
Bx = np.zeros([
layout.allocSize(tv.interpOrder, tv.BxCentering[0], tv.nbrCells[0]),
layout.allocSize(tv.interpOrder, tv.BxCentering[1], tv.nbrCells[1])
],
dtype=np.float64)
By = np.zeros([
layout.allocSize(tv.interpOrder, tv.ByCentering[0], tv.nbrCells[0]),
layout.allocSize(tv.interpOrder, tv.ByCentering[1], tv.nbrCells[1])
],
dtype=np.float64)
Bz = np.zeros([
layout.allocSize(tv.interpOrder, tv.BzCentering[0], tv.nbrCells[0]),
layout.allocSize(tv.interpOrder, tv.BzCentering[1], tv.nbrCells[1])
],
dtype=np.float64)
Jx = np.zeros([
layout.allocSize(tv.interpOrder, tv.JxCentering[0], tv.nbrCells[0]),
layout.allocSize(tv.interpOrder, tv.JxCentering[1], tv.nbrCells[1])
],
dtype=np.float64)
Jy = np.zeros([
layout.allocSize(tv.interpOrder, tv.JyCentering[0], tv.nbrCells[0]),
layout.allocSize(tv.interpOrder, tv.JyCentering[1], tv.nbrCells[1])
],
dtype=np.float64)
Jz = np.zeros([
layout.allocSize(tv.interpOrder, tv.JzCentering[0], tv.nbrCells[0]),
layout.allocSize(tv.interpOrder, tv.JzCentering[1], tv.nbrCells[1])
],
dtype=np.float64)
w1 = np.zeros_like(Jz)
w2 = np.zeros_like(Jz)
psi_p_X = layout.physicalStartIndex(tv.interpOrder, 'primal')
pei_p_X = layout.physicalEndIndex(tv.interpOrder, 'primal', tv.nbrCells[0])
psi_p_Y = layout.physicalStartIndex(tv.interpOrder, 'primal')
pei_p_Y = layout.physicalEndIndex(tv.interpOrder, 'primal', tv.nbrCells[1])
psi_d_X = layout.physicalStartIndex(tv.interpOrder, 'dual')
pei_d_X = layout.physicalEndIndex(tv.interpOrder, 'dual', tv.nbrCells[0])
psi_d_Y = layout.physicalStartIndex(tv.interpOrder, 'dual')
pei_d_Y = layout.physicalEndIndex(tv.interpOrder, 'dual', tv.nbrCells[1])
nbrGhost_p = layout.nbrGhosts(tv.interpOrder, 'primal')
nbrGhost_d = layout.nbrGhosts(tv.interpOrder, 'dual')
x_dual = tv.meshSize[0] * np.arange(
layout.allocSize(tv.interpOrder, 'dual', tv.nbrCells[0])
) - tv.meshSize[0] * nbrGhost_d + tv.meshSize[0] * 0.5
y_dual = tv.meshSize[1] * np.arange(
layout.allocSize(tv.interpOrder, 'dual', tv.nbrCells[1])
) - tv.meshSize[1] * nbrGhost_d + tv.meshSize[1] * 0.5
x_primal = tv.meshSize[0] * np.arange(
layout.allocSize(tv.interpOrder, 'primal',
tv.nbrCells[0])) - tv.meshSize[0] * nbrGhost_p
y_primal = tv.meshSize[1] * np.arange(
layout.allocSize(tv.interpOrder, 'primal',
tv.nbrCells[1])) - tv.meshSize[1] * nbrGhost_p
Bx = np.tensordot(np.cos(2 * np.pi / tv.domainSize[0] * x_primal),
np.sin(2 * np.pi / tv.domainSize[1] * y_dual),
axes=0)
By = np.tensordot(np.cos(2 * np.pi / tv.domainSize[0] * x_dual),
np.tanh(2 * np.pi / tv.domainSize[1] * y_primal),
axes=0)
Bz = np.tensordot(np.sin(2 * np.pi / tv.domainSize[0] * x_dual),
np.tanh(2 * np.pi / tv.domainSize[1] * y_dual),
axes=0)
# Jx = dyBz
# Jy = -dxBz
# Jz = dxBy - dyBx
Jx[:,
psi_p_Y:pei_p_Y + 1] = (Bz[:, psi_d_Y:pei_d_Y + 2] -
Bz[:, psi_d_Y - 1:pei_d_Y + 1]) / tv.meshSize[1]
Jy[psi_p_X:pei_p_X +
1, :] = -(Bz[psi_d_X:pei_d_X + 2, :] -
Bz[psi_d_X - 1:pei_d_X + 1, :]) / tv.meshSize[0]
w1[psi_p_X:pei_p_X +
1, :] = (By[psi_d_X:pei_d_X + 2, :] -
By[psi_d_X - 1:pei_d_X + 1, :]) / tv.meshSize[0]
w2[:, psi_p_Y:pei_p_Y +
1] = -(Bx[:, psi_d_Y:pei_d_Y + 2] -
Bx[:, psi_d_Y - 1:pei_d_Y + 1]) / tv.meshSize[1]
Jz = w1 + w2
filename_jx = "jx_yee_2D_order1.txt"
filename_jy = "jy_yee_2D_order1.txt"
filename_jz = "jz_yee_2D_order1.txt"
np.savetxt(os.path.join(path, filename_jx), Jx.flatten('C'), delimiter=" ")
np.savetxt(os.path.join(path, filename_jy), Jy.flatten('C'), delimiter=" ")
np.savetxt(os.path.join(path, filename_jz), Jz.flatten('C'), delimiter=" ")
