def _calcValue(self):
Nfaces = self.mesh.numberOfFaces
M = self.mesh._maxFacesPerCell
dim = self.mesh.dim
cellFaceIDs = self.mesh.cellFaceIDs
faceNormalAreas = self.distanceVar._levelSetNormals * self.mesh._faceAreas
cellFaceNormalAreas = numerix.array(MA.filled(numerix.take(faceNormalAreas, cellFaceIDs, axis=-1), 0))
norms = numerix.array(MA.filled(MA.array(self.mesh._cellNormals), 0))
alpha = numerix.dot(cellFaceNormalAreas, norms)
alpha = numerix.where(alpha > 0, alpha, 0)
alphasum = numerix.sum(alpha, axis=0)
alphasum += (alphasum < 1e-100) * 1.0
alpha = alpha / alphasum
phi = numerix.repeat(self.distanceVar[numerix.newaxis, ...], M, axis=0)
alpha = numerix.where(phi > 0., 0, alpha)
volumes = numerix.array(self.mesh.cellVolumes)
alpha = alpha * volumes * norms
value = numerix.zeros((dim, Nfaces), 'd')
vector._putAdd(value, cellFaceIDs, alpha, mask=MA.getmask(MA.array(cellFaceIDs)))
## value = numerix.reshape(value, (dim, Nfaces, dim))
return -value / self.mesh._faceAreas
def _getDifferences(self, adjacentValues, cellValues, oldArray, cellToCellIDs, mesh):
dAP = mesh._cellToCellDistances
## adjacentGradient = numerix.take(oldArray.grad, cellToCellIDs)
adjacentGradient = numerix.take(oldArray.grad, mesh._cellToCellIDs, axis=-1)
adjacentNormalGradient = numerix.dot(adjacentGradient, mesh._cellNormals)
adjacentUpValues = cellValues + 2 * dAP * adjacentNormalGradient
cellIDs = numerix.repeat(numerix.arange(mesh.numberOfCells)[numerix.newaxis, ...],
mesh._maxFacesPerCell, axis=0)
cellIDs = MA.masked_array(cellIDs, mask = MA.getmask(mesh._cellToCellIDs))
cellGradient = numerix.take(oldArray.grad, cellIDs, axis=-1)
cellNormalGradient = numerix.dot(cellGradient, mesh._cellNormals)
cellUpValues = adjacentValues - 2 * dAP * cellNormalGradient
cellLaplacian = (cellUpValues + adjacentValues - 2 * cellValues) / dAP**2
adjacentLaplacian = (adjacentUpValues + cellValues - 2 * adjacentValues) / dAP**2
adjacentLaplacian = adjacentLaplacian.filled(0)
cellLaplacian = cellLaplacian.filled(0)
mm = numerix.where(cellLaplacian * adjacentLaplacian < 0.,
0.,
numerix.where(abs(cellLaplacian) > abs(adjacentLaplacian),
adjacentLaplacian,
cellLaplacian))
return FirstOrderAdvectionTerm._getDifferences(self, adjacentValues, cellValues, oldArray, cellToCellIDs, mesh) - mm * dAP / 2.
def _calcValue_(self, alpha, id1, id2):
cell1 = numerix.take(self.var, id1, axis=-1)
cell2 = numerix.take(self.var, id2, axis=-1)
return numerix.where((cell1 > 0) & (cell2 > 0),
numerix.minimum(cell1, cell2),
numerix.where((cell1 < 0) & (cell2 < 0),
numerix.maximum(cell1, cell2), 0))
def _calcValue(self):
"""
Test case added because `and` was being used instead of bitwise `&`.
>>> from fipy.meshes import Grid1D
>>> mesh = Grid1D(nx = 3)
>>> from fipy.variables.faceVariable import FaceVariable
>>> P = FaceVariable(mesh = mesh, value = (1e-3, 1e+71, 1e-3, 1e-3))
>>> alpha = ExponentialConvectionTerm([1])._alpha(P)
>>> print alpha
[ 0.5 1. 0.5 0.5]
"""
eps = 1e-3
largeValue = 101.0
P = self.P.numericValue
P = numerix.where(abs(P) < eps, eps, P)
alpha = numerix.where(P > largeValue, (P - 1) / P, 0.5)
Pmin = numerix.where(P > largeValue + 1, largeValue + 1, P)
alpha = numerix.where((abs(Pmin) > eps) & (Pmin <= largeValue),
((Pmin - 1) * numerix.exp(Pmin) + 1) /
(Pmin * (numerix.exp(Pmin) - 1)), alpha)
return alpha
def __getRotationTensor(self, mesh):
if not hasattr(self, 'rotationTensor'):
rotationTensor = FaceVariable(mesh=mesh, rank=2)
rotationTensor[:, 0] = self._getNormals(mesh)
if mesh.dim == 2:
rotationTensor[:, 1] = rotationTensor[:, 0].dot(
(((0, 1), (-1, 0))))
elif mesh.dim == 3:
epsilon = 1e-20
div = numerix.sqrt(1 - rotationTensor[2, 0]**2)
flag = numerix.resize(div > epsilon,
(mesh.dim, mesh.numberOfFaces))
rotationTensor[0, 1] = 1
rotationTensor[:, 1] = numerix.where(
flag, rotationTensor[:, 0].dot(
(((0, 1, 0), (-1, 0, 0), (0, 0, 0)))) / div,
rotationTensor[:, 1])
rotationTensor[1, 2] = 1
rotationTensor[:, 2] = numerix.where(
flag, rotationTensor[:, 0] * rotationTensor[2, 0] / div,
rotationTensor[:, 2])
rotationTensor[2, 2] = -div
self.rotationTensor = rotationTensor
return self.rotationTensor
def _getRotationTensor(self, mesh):
if not hasattr(self, 'rotationTensor'):
from fipy.variables.faceVariable import FaceVariable
rotationTensor = FaceVariable(mesh=mesh, rank=2)
rotationTensor[:, 0] = self._getNormals(mesh)
if mesh.getDim() == 2:
rotationTensor[:,1] = rotationTensor[:,0].dot((((0, 1), (-1, 0))))
elif mesh.getDim() ==3:
epsilon = 1e-20
div = numerix.sqrt(1 - rotationTensor[2,0]**2)
flag = numerix.resize(div > epsilon, (mesh.getDim(), mesh._getNumberOfFaces()))
rotationTensor[0, 1] = 1
rotationTensor[:, 1] = numerix.where(flag,
rotationTensor[:,0].dot((((0, 1, 0), (-1, 0, 0), (0, 0, 0)))) / div,
rotationTensor[:, 1])
rotationTensor[1, 2] = 1
rotationTensor[:, 2] = numerix.where(flag,
rotationTensor[:,0] * rotationTensor[2,0] / div,
rotationTensor[:, 2])
rotationTensor[2, 2] = -div
self.rotationTensor = rotationTensor
return self.rotationTensor
def _calcValuePy(self, eps, P):
"""
Test case added because `and` was being used instead of bitwise `&`.
>>> from fipy.meshes.grid1D import Grid1D
>>> mesh = Grid1D(nx = 3)
>>> from fipy.variables.faceVariable import FaceVariable
>>> P = FaceVariable(mesh = mesh, value = (1e-3, 1e+71, 1e-3, 1e-3))
>>> alpha = PowerLawConvectionTerm._Alpha(P)
>>> print numerix.allclose(alpha, [ 0.5, 1., 0.5 , 0.5])
True
"""
P = numerix.where(abs(P) < eps, eps, P)
alpha = numerix.where( P > 10., (P - 1.) / P, 0.5)
tmp = (1. - P / 10.)
tmpSqr = tmp * tmp
alpha = numerix.where( (10. >= P) & (P > eps), ((P-1.) + tmpSqr*tmpSqr*tmp) / P, alpha)
tmp = (1. + P / 10.)
tmpSqr = tmp * tmp
alpha = numerix.where((-eps > P) & (P >= -10.), (tmpSqr*tmpSqr*tmp - 1.) / P, alpha)
alpha = numerix.where( P < -10., -1. / P, alpha)
return PhysicalField(value = alpha)
def _orderVertices(vertexCoords, vertices):
coordinates = numerix.take(vertexCoords, vertices, axis=1)
centroid = numerix.add.reduce(coordinates, axis=1) / coordinates.shape[1]
coordinates = coordinates - centroid[..., numerix.newaxis]
coordinates = numerix.where(coordinates == 0, 1.e-10, coordinates) ## to prevent division by zero
angles = numerix.arctan(coordinates[1] / coordinates[0]) + numerix.where(coordinates[0] < 0, numerix.pi, 0) ## angles go from -pi / 2 to 3*pi / 2
sortorder = numerix.argsort(angles)
return numerix.take(vertices, sortorder)
def _calcValue_(self, alpha, id1, id2):
cell1 = numerix.take(self.var,id1, axis=-1)
cell2 = numerix.take(self.var,id2, axis=-1)
return numerix.where((cell1 > 0) & (cell2 > 0),
numerix.minimum(cell1, cell2),
numerix.where((cell1 < 0) & (cell2 < 0),
numerix.maximum(cell1, cell2),
0))
def _calcValue(self):
eps = 1e-3
P = self.P
alpha = numerix.where( P > 2., (P - 1) / P, 0.)
alpha = numerix.where( numerix.logical_and(2. >= P, P >= -2.), 0.5, alpha)
alpha = numerix.where( -2. > P, -1 / P, alpha)
return alpha
def __init__(self,
trenchDepth=None,
trenchSpacing=None,
boundaryLayerDepth=None,
cellSize=None,
aspectRatio=None,
angle=0.,
communicator=parallelComm):
"""
`trenchDepth` - Depth of the trench.
`trenchSpacing` - The distance between the trenches.
`boundaryLayerDepth` - The depth of the hydrodynamic boundary
layer.
`cellSize` - The cell Size.
`aspectRatio` - trenchDepth / trenchWidth
`angle` - The angle for the taper of the trench.
The trench mesh takes the parameters generally used to define
a trench region and recasts then for the general
`GapFillMesh`.
"""
heightBelowTrench = cellSize * 10.
heightAboveTrench = trenchDepth / 1.
fineRegionHeight = heightBelowTrench + trenchDepth + heightAboveTrench
transitionHeight = fineRegionHeight * 3.
domainWidth = trenchSpacing / 2.
domainHeight = heightBelowTrench + trenchDepth + boundaryLayerDepth
super(TrenchMesh, self).__init__(cellSize=cellSize,
desiredDomainWidth=domainWidth,
desiredDomainHeight=domainHeight,
desiredFineRegionHeight=fineRegionHeight,
transitionRegionHeight=transitionHeight,
communicator=parallelComm)
trenchWidth = trenchDepth / aspectRatio
x, y = self.cellCenters
Y = (y - (heightBelowTrench + trenchDepth / 2))
taper = numerix.tan(angle) * Y
self.electrolyteMask = numerix.where(y > trenchDepth + heightBelowTrench,
1,
numerix.where(y < heightBelowTrench,
0,
numerix.where(x > trenchWidth / 2 + taper,
0,
1)))
def __init__(self,
trenchDepth=None,
trenchSpacing=None,
boundaryLayerDepth=None,
cellSize=None,
aspectRatio=None,
angle=0.,
communicator=parallelComm):
"""
`trenchDepth` - Depth of the trench.
`trenchSpacing` - The distance between the trenches.
`boundaryLayerDepth` - The depth of the hydrodynamic boundary
layer.
`cellSize` - The cell Size.
`aspectRatio` - trenchDepth / trenchWidth
`angle` - The angle for the taper of the trench.
The trench mesh takes the parameters generally used to define
a trench region and recasts then for the general
`GapFillMesh`.
"""
heightBelowTrench = cellSize * 10.
heightAboveTrench = trenchDepth / 1.
fineRegionHeight = heightBelowTrench + trenchDepth + heightAboveTrench
transitionHeight = fineRegionHeight * 3.
domainWidth = trenchSpacing / 2.
domainHeight = heightBelowTrench + trenchDepth + boundaryLayerDepth
super(TrenchMesh, self).__init__(cellSize=cellSize,
desiredDomainWidth=domainWidth,
desiredDomainHeight=domainHeight,
desiredFineRegionHeight=fineRegionHeight,
transitionRegionHeight=transitionHeight,
communicator=parallelComm)
trenchWidth = trenchDepth / aspectRatio
x, y = self.cellCenters
Y = (y - (heightBelowTrench + trenchDepth / 2))
taper = numerix.tan(angle) * Y
self.electrolyteMask = numerix.where(y > trenchDepth + heightBelowTrench,
1,
numerix.where(y < heightBelowTrench,
0,
numerix.where(x > trenchWidth / 2 + taper,
0,
1)))
def _calcValue(self):
eps = 1e-3
P = self.P
alpha = numerix.where( P > 2., (P - 1) / P, 0.)
alpha = numerix.where( numerix.logical_and(2. >= P, P >= -2.), 0.5, alpha)
alpha = numerix.where( -2. > P, -1 / P, alpha)
return alpha
def _orderVertices(vertexCoords, vertices):
coordinates = numerix.take(vertexCoords, vertices)
centroid = numerix.add.reduce(coordinates) / coordinates.shape[0]
coordinates = coordinates - centroid
# to prevent division by zero
coordinates = numerix.where(coordinates == 0, 1.e-100, coordinates)
# angles go from -pi / 2 to 3*pi / 2
angles = numerix.arctan(coordinates[:, 1] / coordinates[:, 0]) \
+ numerix.where(coordinates[:, 0] < 0, numerix.pi, 0)
sortorder = numerix.argsort(angles)
return numerix.take(vertices, sortorder)
def _orderVertices(vertexCoords, vertices):
coordinates = numerix.take(vertexCoords, vertices)
centroid = numerix.add.reduce(coordinates) / coordinates.shape[0]
coordinates = coordinates - centroid
# to prevent division by zero
coordinates = numerix.where(coordinates == 0, 1.e-100, coordinates)
# angles go from -pi / 2 to 3*pi / 2
angles = numerix.arctan(coordinates[:, 1] / coordinates[:, 0]) \
+ numerix.where(coordinates[:, 0] < 0, numerix.pi, 0)
sortorder = numerix.argsort(angles)
return numerix.take(vertices, sortorder)
def _getGradient(self, normalGradient, gradUpwind):
gradUpUpwind = -gradUpwind + 2 * normalGradient
avg = 0.5 * (abs(gradUpwind) + abs(gradUpUpwind))
min3 = numerix.minimum(
numerix.minimum(abs(2 * gradUpwind), abs(2 * gradUpUpwind)), avg)
grad = numerix.where(gradUpwind * gradUpUpwind < 0., 0.,
numerix.where(gradUpUpwind > 0., min3, -min3))
return grad
def _getGradient(self, normalGradient, gradUpwind):
gradUpUpwind = -gradUpwind + 2 * normalGradient
avg = 0.5 * (abs(gradUpwind) + abs(gradUpUpwind))
min3 = numerix.minimum(numerix.minimum(abs(gradUpwind), abs(gradUpUpwind)), avg)
grad = numerix.where(gradUpwind * gradUpUpwind < 0.,
0.,
numerix.where(gradUpUpwind > 0.,
min3,
-min3))
return grad
def _calcValue_(self, alpha, id1, id2):
distance = numerix.array(self.var)
cell1 = numerix.take(distance, id1)
cell2 = numerix.take(distance, id2)
return numerix.where(numerix.logical_or(cell1 < 0, cell2 < 0), 0,
self.diffusionCoeff)
def _levelSetNormals(self):
"""
Return the face level set normals.
>>> from fipy.meshes import Grid2D
>>> from fipy.variables.faceVariable import FaceVariable
>>> mesh = Grid2D(dx = .5, dy = .5, nx = 2, ny = 2)
>>> distanceVariable = DistanceVariable(mesh = mesh,
... value = (-0.5, 0.5, 0.5, 1.5))
>>> v = 1 / numerix.sqrt(2)
>>> answer = FaceVariable(mesh=mesh,
... value=((0, 0, v, v, 0, 0, 0, v, 0, 0, v, 0),
... (0, 0, v, v, 0, 0, 0, v, 0, 0, v, 0)))
>>> print numerix.allclose(distanceVariable._levelSetNormals, answer)
True
"""
faceGrad = self.grad.arithmeticFaceValue
faceGradMag = numerix.array(faceGrad.mag)
faceGradMag = numerix.where(faceGradMag > 1e-10,
faceGradMag,
1e-10)
faceGrad = numerix.array(faceGrad)
## set faceGrad zero on exteriorFaces
exteriorFaces = self.mesh.exteriorFaces
if len(exteriorFaces.value) > 0:
faceGrad[..., exteriorFaces.value] = 0.
return faceGrad / faceGradMag
def _interfaceNormals(self):
"""
Returns the normals on the boundary faces only, the other are set to zero.
>>> from fipy.meshes import Grid2D
>>> from fipy.variables.faceVariable import FaceVariable
>>> mesh = Grid2D(dx = .5, dy = .5, nx = 2, ny = 2)
>>> distanceVariable = DistanceVariable(mesh = mesh,
... value = (-0.5, 0.5, 0.5, 1.5))
>>> v = 1 / numerix.sqrt(2)
>>> answer = FaceVariable(mesh=mesh,
... value=((0, 0, v, 0, 0, 0, 0, v, 0, 0, 0, 0),
... (0, 0, v, 0, 0, 0, 0, v, 0, 0, 0, 0)))
>>> print numerix.allclose(distanceVariable._interfaceNormals, answer)
True
"""
M = self.mesh.dim
interfaceFlag = numerix.repeat(self._interfaceFlag[numerix.newaxis,
...],
M,
axis=0)
return numerix.where(interfaceFlag, self._levelSetNormals, 0)
def _levelSetNormals(self):
"""
Return the face level set normals.
>>> from fipy.meshes import Grid2D
>>> from fipy.variables.faceVariable import FaceVariable
>>> mesh = Grid2D(dx = .5, dy = .5, nx = 2, ny = 2)
>>> distanceVariable = DistanceVariable(mesh = mesh,
... value = (-0.5, 0.5, 0.5, 1.5))
>>> v = 1 / numerix.sqrt(2)
>>> answer = FaceVariable(mesh=mesh,
... value=((0, 0, v, v, 0, 0, 0, v, 0, 0, v, 0),
... (0, 0, v, v, 0, 0, 0, v, 0, 0, v, 0)))
>>> print numerix.allclose(distanceVariable._levelSetNormals, answer)
True
"""
faceGrad = self.grad.arithmeticFaceValue
faceGradMag = numerix.array(faceGrad.mag)
faceGradMag = numerix.where(faceGradMag > 1e-10, faceGradMag, 1e-10)
faceGrad = numerix.array(faceGrad)
## set faceGrad zero on exteriorFaces
exteriorFaces = self.mesh.exteriorFaces
if len(exteriorFaces.value) > 0:
faceGrad[..., exteriorFaces.value] = 0.
return faceGrad / faceGradMag
def _plot(self):
var = self.vars[0]
mesh = var.mesh
U, V = var.numericValue
U = numerix.take(U, self.indices)
V = numerix.take(V, self.indices)
ang = numerix.arctan2(V, U)
mag = numerix.sqrt(U**2 + V**2)
datamin, datamax = self._autoscale(vars=(mag,),
datamin=self._getLimit('datamin'),
datamax=self._getLimit('datamax'))
mag = numerix.where(mag > datamax, datamax, mag)
mag = numerix.ma.masked_array(mag, mag < datamin)
if self.log:
mag = numerix.log10(mag)
mag = numerix.ma.masked_array(mag, numerix.isnan(mag))
U = mag * numerix.cos(ang)
V = mag * numerix.sin(ang)
self._quiver.set_UVC(U, V)
self.axes.set_xlim(xmin=self._getLimit('xmin'),
xmax=self._getLimit('xmax'))
self.axes.set_ylim(ymin=self._getLimit('ymin'),
ymax=self._getLimit('ymax'))
def _calcValue(self):
flag = MA.filled(
numerix.take(self.distanceVar._interfaceFlag,
self.mesh.cellFaceIDs), 0)
flag = numerix.sum(flag, axis=0)
return numerix.where(
numerix.logical_and(self.distanceVar.value > 0, flag > 0), 1, 0)
def _plot(self):
var = self.vars[0]
mesh = var.mesh
U, V = var.numericValue
U = numerix.take(U, self.indices)
V = numerix.take(V, self.indices)
ang = numerix.arctan2(V, U)
mag = numerix.sqrt(U**2 + V**2)
datamin, datamax = self._autoscale(vars=(mag, ),
datamin=self._getLimit('datamin'),
datamax=self._getLimit('datamax'))
mag = numerix.where(mag > datamax, datamax, mag)
mag = numerix.ma.masked_array(mag, mag < datamin)
if self.log:
mag = numerix.log10(mag)
mag = numerix.ma.masked_array(mag, numerix.isnan(mag))
U = mag * numerix.cos(ang)
V = mag * numerix.sin(ang)
self._quiver.set_UVC(U, V)
self.axes.set_xlim(xmin=self._getLimit('xmin'),
xmax=self._getLimit('xmax'))
self.axes.set_ylim(ymin=self._getLimit('ymin'),
ymax=self._getLimit('ymax'))
def run(self):
MayaviDaemon._viewers.append(self)
mlab.clf()
self.cellsource = self.setup_source(self.cellfname)
self.has_cell, bounds = self._examine_data(source=self.cellsource,
datatype="cell_data",
bounds=zeros((0, 6), 'l'))
self.facesource = self.setup_source(self.facefname)
self.has_face, bounds = self._examine_data(source=self.facesource,
datatype="point_data",
bounds=bounds)
boundsmin = bounds.min(axis=0)
boundsmax = bounds.max(axis=0)
bounds = (boundsmin[0], boundsmax[1], boundsmin[2], boundsmax[3],
boundsmin[4], boundsmax[5])
self.bounds = where(self.bounds == array((None, )), bounds,
self.bounds).astype(float)
self.view_data()
# Poll the lock file.
self.timer = Timer(1000 / self.fps, self.poll_file)
def _calcValue_(self, alpha, id1, id2):
cell1 = take(self.var, id1)
cell2 = take(self.var, id2)
delta = cell1 - cell2
eps = 1e-14
value = where(abs(delta) < eps, 1.0 / exp(delta), 0.0)
delta = where(abs(delta) < eps, eps, delta)
value = where((abs(delta) > eps) & (delta < 100), delta / (exp(delta) - 1), value)
value *= exp(cell1)
for bc in self.bcs:
if isinstance(bc, FixedValue):
value[bc.faces.value] = bc._value
return value
def _calcValue_(self, alpha, id1, id2):
distance = numerix.array(self.var)
cell1 = numerix.take(distance, id1)
cell2 = numerix.take(distance, id2)
return numerix.where(numerix.logical_or(cell1 < 0, cell2 < 0),
0,
self.diffusionCoeff)
def _calcValue(self):
eps = self.eps
P = self.P.numericValue
P = numerix.where(abs(P) < eps, eps, P)
alpha = numerix.where( P > 10., (P - 1.) / P, 0.5)
tmp = (1. - P / 10.)
tmpSqr = tmp * tmp
alpha = numerix.where( (10. >= P) & (P > eps), ((P-1.) + tmpSqr*tmpSqr*tmp) / P, alpha)
tmp = (1. + P / 10.)
tmpSqr = tmp * tmp
alpha = numerix.where((-eps > P) & (P >= -10.), (tmpSqr*tmpSqr*tmp - 1.) / P, alpha)
alpha = numerix.where( P < -10., -1. / P, alpha)
return PhysicalField(value = alpha)
def _calcValue(self):
eps = self.eps
P = self.P.numericValue
P = numerix.where(abs(P) < eps, eps, P)
alpha = numerix.where( P > 10., (P - 1.) / P, 0.5)
tmp = (1. - P / 10.)
tmpSqr = tmp * tmp
alpha = numerix.where( (10. >= P) & (P > eps), ((P-1.) + tmpSqr*tmpSqr*tmp) / P, alpha)
tmp = (1. + P / 10.)
tmpSqr = tmp * tmp
alpha = numerix.where((-eps > P) & (P >= -10.), (tmpSqr*tmpSqr*tmp - 1.) / P, alpha)
alpha = numerix.where( P < -10., -1. / P, alpha)
return PhysicalField(value = alpha)
def _calcValue_(self, alpha, id1, id2):
cell1 = take(self.var,id1)
cell2 = take(self.var,id2)
delta = cell1 - cell2
eps = 1e-14
value = where(abs(delta) < eps, 1. / exp(delta), 0.)
delta = where(abs(delta) < eps, eps, delta)
value = where((abs(delta) > eps) & (delta < 100),
delta / (exp(delta) - 1), value)
value *= exp(cell1)
for bc in self.bcs:
if isinstance(bc, FixedValue):
value[bc.faces.value] = bc._value
return value
def _buildMatrix(self,
var,
SparseMatrix,
boundaryConditions=(),
dt=None,
transientGeomCoeff=None,
diffusionGeomCoeff=None):
var, L, b = FaceTerm._buildMatrix(
self,
var,
SparseMatrix,
boundaryConditions=boundaryConditions,
dt=dt,
transientGeomCoeff=transientGeomCoeff,
diffusionGeomCoeff=diffusionGeomCoeff)
## if var.rank != 1:
mesh = var.mesh
if (not hasattr(self, 'constraintL')) or (not hasattr(
self, 'constraintB')):
weight = self._getWeight(var, transientGeomCoeff,
diffusionGeomCoeff)
if 'implicit' in weight:
alpha = weight['implicit']['cell 1 diag']
else:
alpha = 0.0
alpha_constraint = numerix.where(var.faceGrad.constraintMask, 1.0,
alpha)
def divergence(face_value):
return (
face_value * \
(var.faceGrad.constraintMask | var.arithmeticFaceValue.constraintMask) * \
self.coeff * mesh.exteriorFaces
).divergence * mesh.cellVolumes
self.constraintL = divergence(alpha_constraint)
dvar = (var.faceGrad * mesh._cellDistances *
mesh.faceNormals).sum(axis=0)
self.constraintB = divergence(
(alpha_constraint - 1) * var.arithmeticFaceValue +
(alpha - 1) * dvar * var.faceGrad.constraintMask)
ids = self._reshapeIDs(var, numerix.arange(mesh.numberOfCells))
L.addAt(
numerix.array(self.constraintL).ravel(), ids.ravel(),
ids.swapaxes(0, 1).ravel())
b += numerix.reshape(self.constraintB.value, ids.shape).sum(0).ravel()
return (var, L, b)
def run(self):
MayaviDaemon._viewers.append(self)
mlab.clf()
bounds = zeros((0, 6), 'l')
self.cellsource = self.setup_source(self.cellfname)
if self.cellsource is not None:
tmp = [out.cell_data.scalars for out in self.cellsource.outputs \
if out.cell_data.scalars is not None]
self.has_cell_scalars = (len(tmp) > 0)
tmp = [out.cell_data.vectors for out in self.cellsource.outputs \
if out.cell_data.vectors is not None]
self.has_cell_vectors = (len(tmp) > 0)
tmp = [out.cell_data.tensors for out in self.cellsource.outputs \
if out.cell_data.tensors is not None]
self.has_cell_tensors = (len(tmp) > 0)
bounds = concatenate((bounds,
[out.bounds for out in self.cellsource.outputs]),
axis=0)
self.facesource = self.setup_source(self.facefname)
if self.facesource is not None:
tmp = [out.point_data.scalars for out in self.facesource.outputs \
if out.point_data.scalars is not None]
self.has_face_scalars = (len(tmp) > 0)
tmp = [out.point_data.vectors for out in self.facesource.outputs \
if out.point_data.vectors is not None]
self.has_face_vectors = (len(tmp) > 0)
tmp = [out.point_data.tensors for out in self.facesource.outputs \
if out.point_data.tensors is not None]
self.has_face_tensors = (len(tmp) > 0)
bounds = concatenate((bounds,
[out.bounds for out in self.facesource.outputs]),
axis=0)
boundsmin = bounds.min(axis=0)
boundsmax = bounds.max(axis=0)
bounds = (boundsmin[0], boundsmax[1],
boundsmin[2], boundsmax[3],
boundsmin[4], boundsmax[5])
self.bounds = where(self.bounds == array((None,)),
bounds,
self.bounds).astype(float)
self.view_data()
# Poll the lock file.
self.timer = Timer(1000 / self.fps, self.poll_file)
def run(self):
MayaviDaemon._viewers.append(self)
mlab.clf()
bounds = zeros((0, 6), 'l')
self.cellsource = self.setup_source(self.cellfname)
if self.cellsource is not None:
tmp = [out.cell_data.scalars for out in self.cellsource.outputs \
if out.cell_data.scalars is not None]
self.has_cell_scalars = (len(tmp) > 0)
tmp = [out.cell_data.vectors for out in self.cellsource.outputs \
if out.cell_data.vectors is not None]
self.has_cell_vectors = (len(tmp) > 0)
tmp = [out.cell_data.tensors for out in self.cellsource.outputs \
if out.cell_data.tensors is not None]
self.has_cell_tensors = (len(tmp) > 0)
bounds = concatenate((bounds,
[out.bounds for out in self.cellsource.outputs]),
axis=0)
self.facesource = self.setup_source(self.facefname)
if self.facesource is not None:
tmp = [out.point_data.scalars for out in self.facesource.outputs \
if out.point_data.scalars is not None]
self.has_face_scalars = (len(tmp) > 0)
tmp = [out.point_data.vectors for out in self.facesource.outputs \
if out.point_data.vectors is not None]
self.has_face_vectors = (len(tmp) > 0)
tmp = [out.point_data.tensors for out in self.facesource.outputs \
if out.point_data.tensors is not None]
self.has_face_tensors = (len(tmp) > 0)
bounds = concatenate((bounds,
[out.bounds for out in self.facesource.outputs]),
axis=0)
boundsmin = bounds.min(axis=0)
boundsmax = bounds.max(axis=0)
bounds = (boundsmin[0], boundsmax[1],
boundsmin[2], boundsmax[3],
boundsmin[4], boundsmax[5])
self.bounds = where(self.bounds == array((None,)),
bounds,
self.bounds).astype(float)
self.view_data()
# Poll the lock file.
self.timer = Timer(1000 / self.fps, self.poll_file)
def _getDifferences(self, adjacentValues, cellValues, oldArray,
cellToCellIDs, mesh):
dAP = mesh._cellToCellDistances
## adjacentGradient = numerix.take(oldArray.grad, cellToCellIDs)
adjacentGradient = numerix.take(oldArray.grad,
mesh._cellToCellIDs,
axis=-1)
adjacentNormalGradient = numerix.dot(adjacentGradient,
mesh._cellNormals)
adjacentUpValues = cellValues + 2 * dAP * adjacentNormalGradient
cellIDs = numerix.repeat(numerix.arange(
mesh.numberOfCells)[numerix.newaxis, ...],
mesh._maxFacesPerCell,
axis=0)
cellIDs = MA.masked_array(cellIDs,
mask=MA.getmask(mesh._cellToCellIDs))
cellGradient = numerix.take(oldArray.grad, cellIDs, axis=-1)
cellNormalGradient = numerix.dot(cellGradient, mesh._cellNormals)
cellUpValues = adjacentValues - 2 * dAP * cellNormalGradient
cellLaplacian = (cellUpValues + adjacentValues -
2 * cellValues) / dAP**2
adjacentLaplacian = (adjacentUpValues + cellValues -
2 * adjacentValues) / dAP**2
adjacentLaplacian = adjacentLaplacian.filled(0)
cellLaplacian = cellLaplacian.filled(0)
mm = numerix.where(
cellLaplacian * adjacentLaplacian < 0., 0.,
numerix.where(
abs(cellLaplacian) > abs(adjacentLaplacian), adjacentLaplacian,
cellLaplacian))
return FirstOrderAdvectionTerm._getDifferences(
self, adjacentValues, cellValues, oldArray, cellToCellIDs,
mesh) - mm * dAP / 2.
def _calcFaceCellToCellNormals(self):
faceCellCentersUp = numerix.take(self._cellCenters, self.faceCellIDs[1], axis=1)
faceCellCentersDown = numerix.take(self._cellCenters, self.faceCellIDs[0], axis=1)
faceCellCentersUp = numerix.where(MA.getmaskarray(faceCellCentersUp),
self._faceCenters,
faceCellCentersUp)
diff = faceCellCentersDown - faceCellCentersUp
mag = numerix.sqrt(numerix.sum(diff**2))
faceCellToCellNormals = diff / numerix.resize(mag, (self.dim, len(mag)))
orientation = 1 - 2 * (numerix.dot(self.faceNormals, faceCellToCellNormals) < 0)
return faceCellToCellNormals * orientation
def _calcFaceAreas(self):
faceVertexIDs = MA.filled(self.faceVertexIDs, -1)
substitute = numerix.repeat(faceVertexIDs[numerix.newaxis, 0],
faceVertexIDs.shape[0], axis=0)
faceVertexIDs = numerix.where(MA.getmaskarray(self.faceVertexIDs), substitute, faceVertexIDs)
faceVertexCoords = numerix.take(self.vertexCoords, faceVertexIDs, axis=1)
faceOrigins = numerix.repeat(faceVertexCoords[:,0], faceVertexIDs.shape[0], axis=0)
faceOrigins = numerix.reshape(faceOrigins, MA.shape(faceVertexCoords))
faceVertexCoords = faceVertexCoords - faceOrigins
left = range(faceVertexIDs.shape[0])
right = left[1:] + [left[0]]
cross = numerix.sum(numerix.cross(faceVertexCoords, numerix.take(faceVertexCoords, right, 1), axis=0), 1)
self.faceAreas = numerix.sqrtDot(cross, cross) / 2.
def _getDiagonalSign(self, transientGeomCoeff=None, diffusionGeomCoeff=None):
if transientGeomCoeff is not None and diffusionGeomCoeff is not None:
diagonalSign = numerix.where(numerix.array(numerix.all(transientGeomCoeff == 0, axis=-1)),
numerix.array(2 * numerix.all(diffusionGeomCoeff[0] <= 0, axis=-1) - 1),
numerix.array(2 * numerix.all(transientGeomCoeff >= 0, axis=-1) - 1))
elif transientGeomCoeff is not None:
diagonalSign = 2 * numerix.all(transientGeomCoeff >= 0, axis=-1) - 1
elif diffusionGeomCoeff is not None:
diagonalSign = 2 * numerix.all(diffusionGeomCoeff[0] <= 0, axis=-1) - 1
else:
diagonalSign = 1
return diagonalSign
def setValue(self, value, unit=None, where=None):
"""
Set the value of the Variable. Can take a masked array.
>>> a = Variable((1,2,3))
>>> a.setValue(5, where=(1, 0, 1))
>>> print a
[5 2 5]
>>> b = Variable((4,5,6))
>>> a.setValue(b, where=(1, 0, 1))
>>> print a
[4 2 6]
>>> print b
[4 5 6]
>>> a.setValue(3)
>>> print a
[3 3 3]
>>> b = numerix.array((3,4,5))
>>> a.setValue(b)
>>> a[:] = 1
>>> print b
[3 4 5]
>>> a.setValue((4,5,6), where=(1, 0))
Traceback (most recent call last):
....
ValueError: shape mismatch: objects cannot be broadcast to a single shape
"""
if where is not None:
tmp = numerix.empty(numerix.getShape(where), self.getsctype())
tmp[:] = value
tmp = numerix.where(where, tmp, self.getValue())
else:
if hasattr(value, 'copy'):
tmp = value.copy()
else:
tmp = value
value = self._makeValue(value=tmp, unit=unit, array=None)
if numerix.getShape(self.value) == ():
self.value.itemset(value)
else:
self.value[:] = value
self._markFresh()
def _calcValue(self):
"""
Test case added because `and` was being used instead of bitwise `&`.
>>> from fipy.meshes import Grid1D
>>> mesh = Grid1D(nx = 3)
>>> from fipy.variables.faceVariable import FaceVariable
>>> P = FaceVariable(mesh = mesh, value = (1e-3, 1e+71, 1e-3, 1e-3))
>>> alpha = ExponentialConvectionTerm([1])._alpha(P)
>>> print(alpha)
[ 0.5 1. 0.5 0.5]
"""
eps = 1e-3
largeValue = 101.0
P = self.P.numericValue
P = numerix.where(abs(P) < eps, eps, P)
alpha = numerix.where(P > largeValue, (P - 1) / P, 0.5)
Pmin = numerix.where(P > largeValue + 1, largeValue + 1, P)
alpha = numerix.where((abs(Pmin) > eps) & (Pmin <= largeValue), ((Pmin - 1) * numerix.exp(Pmin) + 1) / (Pmin * (numerix.exp(Pmin) - 1)), alpha)
return alpha
def _calcFaceAreas(self):
faceVertexIDs = MA.filled(self.faceVertexIDs, -1)
substitute = numerix.repeat(faceVertexIDs[numerix.newaxis, 0],
faceVertexIDs.shape[0], axis=0)
faceVertexIDs = numerix.where(MA.getmaskarray(self.faceVertexIDs),
substitute, faceVertexIDs)
faceVertexCoords = numerix.take(self.vertexCoords, faceVertexIDs, axis=1)
faceOrigins = numerix.repeat(faceVertexCoords[:,0], faceVertexIDs.shape[0], axis=0)
faceOrigins = numerix.reshape(faceOrigins, MA.shape(faceVertexCoords))
faceVertexCoords = faceVertexCoords - faceOrigins
left = range(faceVertexIDs.shape[0])
right = left[1:] + [left[0]]
cross = numerix.sum(numerix.cross(faceVertexCoords,
numerix.take(faceVertexCoords, right, 1),
axis=0),
1)
return numerix.sqrtDot(cross, cross) / 2.
def _getNonOrthogonality(self):
exteriorFaceArray = numerix.zeros((self.faceCellIDs.shape[1],))
numerix.put(exteriorFaceArray, numerix.nonzero(self.getExteriorFaces()), 1)
unmaskedFaceCellIDs = MA.filled(self.faceCellIDs, 0) ## what we put in for the "fill" doesn't matter because only exterior faces have anything masked, and exterior faces have their displacement vectors set to zero.
## if it's an exterior face, make the "displacement vector" equal to zero so the cross product will be zero.
faceDisplacementVectors = numerix.where(numerix.array(zip(exteriorFaceArray, exteriorFaceArray)), 0.0, numerix.take(self._getCellCenters().swapaxes(0,1), unmaskedFaceCellIDs[1, :]) - numerix.take(self._getCellCenters().swapaxes(0,1), unmaskedFaceCellIDs[0, :])).swapaxes(0,1)
faceCrossProducts = (faceDisplacementVectors[0, :] * self.faceNormals[1, :]) - (faceDisplacementVectors[1, :] * self.faceNormals[0, :])
faceDisplacementVectorLengths = numerix.maximum(((faceDisplacementVectors[0, :] ** 2) + (faceDisplacementVectors[1, :] ** 2)) ** 0.5, 1.e-100)
faceWeightedNonOrthogonalities = abs(faceCrossProducts / faceDisplacementVectorLengths) * self.faceAreas
cellFaceWeightedNonOrthogonalities = numerix.take(faceWeightedNonOrthogonalities, self.cellFaceIDs)
cellFaceAreas = numerix.take(self.faceAreas, self.cellFaceIDs)
cellTotalWeightedValues = numerix.add.reduce(cellFaceWeightedNonOrthogonalities, axis = 0)
cellTotalFaceAreas = numerix.add.reduce(cellFaceAreas, axis = 0)
return (cellTotalWeightedValues / cellTotalFaceAreas)
def _getCellInterfaceFlag(self):
"""
Returns 1 for those cells on the interface:
>>> from fipy.meshes.grid2D import Grid2D
>>> from fipy.variables.cellVariable import CellVariable
>>> mesh = Grid2D(dx = .5, dy = .5, nx = 2, ny = 2)
>>> distanceVariable = DistanceVariable(mesh = mesh,
... value = (-0.5, 0.5, 0.5, 1.5))
>>> answer = CellVariable(mesh=mesh, value=(0, 1, 1, 0))
>>> print numerix.allclose(distanceVariable._getCellInterfaceFlag(), answer)
True
"""
flag = MA.filled(numerix.take(self._getInterfaceFlag(), self.cellFaceIDs), 0)
flag = numerix.sum(flag, axis=0)
return numerix.where(numerix.logical_and(self.value > 0, flag > 0), 1, 0)
def _nonOrthogonality(self):
exteriorFaceArray = numerix.zeros((self.faceCellIDs.shape[1], ), 'l')
numerix.put(exteriorFaceArray, numerix.nonzero(self.exteriorFaces), 1)
unmaskedFaceCellIDs = MA.filled(self.faceCellIDs, 0)
# what we put in for the "fill" doesn't matter because only exterior
# faces have anything masked, and exterior faces have their displacement
# vectors set to zero.
#
# if it's an exterior face, make the "displacement vector" equal to zero
# so the cross product will be zero.
faceDisplacementVectors = \
numerix.where(numerix.array(zip(exteriorFaceArray, exteriorFaceArray)),
0.0,
numerix.take(self._scaledCellCenters.swapaxes(0,1),
unmaskedFaceCellIDs[1, :]) \
- numerix.take(self._scaledCellCenters.swapaxes(0,1),
unmaskedFaceCellIDs[0, :]))
faceDisplacementVectors = faceDisplacementVectors.swapaxes(0, 1)
faceCrossProducts = (faceDisplacementVectors[0, :] * self.faceNormals[1,:]) \
- (faceDisplacementVectors[1, :] * self.faceNormals[0, :])
faceDisplacementVectorLengths = numerix.maximum(((faceDisplacementVectors[0, :] ** 2) \
+ (faceDisplacementVectors[1, :] ** 2)) ** 0.5, 1.e-100)
faceWeightedNonOrthogonalities = abs(
faceCrossProducts /
faceDisplacementVectorLengths) * self._faceAreas
cellFaceWeightedNonOrthogonalities = numerix.take(
faceWeightedNonOrthogonalities, self.cellFaceIDs)
cellFaceAreas = numerix.take(self._faceAreas, self.cellFaceIDs)
cellTotalWeightedValues = numerix.add.reduce(
cellFaceWeightedNonOrthogonalities, axis=0)
cellTotalFaceAreas = numerix.add.reduce(cellFaceAreas, axis=0)
return (cellTotalWeightedValues / cellTotalFaceAreas)
def _getDiagonalSign(self,
transientGeomCoeff=None,
diffusionGeomCoeff=None):
if transientGeomCoeff is not None and diffusionGeomCoeff is not None:
diagonalSign = numerix.where(
numerix.array(numerix.all(transientGeomCoeff == 0, axis=-1)),
numerix.array(
2 * numerix.all(diffusionGeomCoeff[0] <= 0, axis=-1) - 1),
numerix.array(2 *
numerix.all(transientGeomCoeff >= 0, axis=-1) -
1))
elif transientGeomCoeff is not None:
diagonalSign = 2 * numerix.all(transientGeomCoeff >= 0,
axis=-1) - 1
elif diffusionGeomCoeff is not None:
diagonalSign = 2 * numerix.all(diffusionGeomCoeff[0] <= 0,
axis=-1) - 1
else:
diagonalSign = 1
return diagonalSign
def _interfaceFlag(self):
"""
Returns 1 for faces on boundary and 0 otherwise.
>>> from fipy.meshes import Grid2D
>>> from fipy.variables.faceVariable import FaceVariable
>>> mesh = Grid2D(dx = .5, dy = .5, nx = 2, ny = 2)
>>> distanceVariable = DistanceVariable(mesh = mesh,
... value = (-0.5, 0.5, 0.5, 1.5))
>>> answer = FaceVariable(mesh=mesh,
... value=(0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0))
>>> print numerix.allclose(distanceVariable._interfaceFlag, answer)
True
"""
adjacentCellIDs = self.mesh._adjacentCellIDs
val0 = numerix.take(numerix.array(self._value), adjacentCellIDs[0])
val1 = numerix.take(numerix.array(self._value), adjacentCellIDs[1])
return numerix.where(val1 * val0 < 0, 1, 0)
def _interfaceFlag(self):
"""
Returns 1 for faces on boundary and 0 otherwise.
>>> from fipy.meshes import Grid2D
>>> from fipy.variables.faceVariable import FaceVariable
>>> mesh = Grid2D(dx = .5, dy = .5, nx = 2, ny = 2)
>>> distanceVariable = DistanceVariable(mesh = mesh,
... value = (-0.5, 0.5, 0.5, 1.5))
>>> answer = FaceVariable(mesh=mesh,
... value=(0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0))
>>> print numerix.allclose(distanceVariable._interfaceFlag, answer)
True
"""
adjacentCellIDs = self.mesh._adjacentCellIDs
val0 = numerix.take(numerix.array(self._value), adjacentCellIDs[0])
val1 = numerix.take(numerix.array(self._value), adjacentCellIDs[1])
return numerix.where(val1 * val0 < 0, 1, 0)
def _interfaceNormals(self):
"""
Returns the normals on the boundary faces only, the other are set to zero.
>>> from fipy.meshes import Grid2D
>>> from fipy.variables.faceVariable import FaceVariable
>>> mesh = Grid2D(dx = .5, dy = .5, nx = 2, ny = 2)
>>> distanceVariable = DistanceVariable(mesh = mesh,
... value = (-0.5, 0.5, 0.5, 1.5))
>>> v = 1 / numerix.sqrt(2)
>>> answer = FaceVariable(mesh=mesh,
... value=((0, 0, v, 0, 0, 0, 0, v, 0, 0, 0, 0),
... (0, 0, v, 0, 0, 0, 0, v, 0, 0, 0, 0)))
>>> print numerix.allclose(distanceVariable._interfaceNormals, answer)
True
"""
M = self.mesh.dim
interfaceFlag = numerix.repeat(self._interfaceFlag[numerix.newaxis, ...], M, axis=0)
return numerix.where(interfaceFlag, self._levelSetNormals, 0)
def getElectrolyteMask(self):
x, y = self.getCellCenters()
Y = (y - (self.heightBelowTrench + self.trenchDepth / 2))
## taper
taper = numerix.tan(self.angle) * Y
## bow
if abs(self.bowWidth) > 1e-12 and (-self.trenchDepth / 2 < Y < self.trenchDepth / 2):
param1 = self.trenchDepth**2 / 8 / self.bowWidth
param2 = self.bowWidth / 2
bow = -numerix.sqrt((param1 + param2)**2 - Y**2) + param1 - param2
else:
bow = 0
## over hang
Y = y - (self.heightBelowTrench + self.trenchDepth - self.overBumpRadius)
overBump = 0
if self.overBumpRadius > 1e-12:
overBump += numerix.where(Y > -self.overBumpRadius,
self.overBumpWidth / 2 * (1 + numerix.cos(Y * numerix.pi / self.overBumpRadius)),
0)
tmp = self.overBumpRadius**2 - Y**2
tmp = (tmp > 0) * tmp
overBump += numerix.where((Y > -self.overBumpRadius) & (Y > 0),
numerix.where(Y > self.overBumpRadius,
-self.overBumpRadius,
-(self.overBumpRadius - numerix.sqrt(tmp))),
0)
return numerix.where(y > self.trenchDepth + self.heightBelowTrench,
1,
numerix.where(y < self.heightBelowTrench,
0,
numerix.where(x > self.trenchWidth / 2 + taper - bow - overBump,
0,
1)))
timeStepDuration = cfl * dx / velocity
distanceVariable.updateOld()
distanceVariable.setValue(numerix.array(distanceVariable) - velocity * timeStepDuration)
surfactantEquation.solve(surfactantVariable)
totalTime += timeStepDuration
distanceViewer.plot()
surfactantViewer.plot()
errorViewer.plot()
finalRadius = initialRadius + totalTime * velocity + distanceVariable
answer = initialSurfactantValue * initialRadius / finalRadius
coverage = surfactantVariable.getInterfaceVar()
error.setValue(numerix.where((coverage > 1e-3) & (distanceVariable > 0), abs(coverage - answer), 0))
adjDistanceVariables = numerix.take(distanceVariable, mesh._getCellToCellIDs())
adjCoverages = numerix.take(coverage, mesh._getCellToCellIDs())
flag = (adjDistanceVariables < 0) & (adjCoverages > 1e-6)
error.setValue(0, where=numerix.sum(flag, index=1) > 0)
del L1[0]
del L2[0]
del Linf[0]
def _plot(self):
from scipy.interpolate import griddata
var = self.vars[0]
mesh = var.mesh
xmin, ymin = mesh.extents['min']
xmax, ymax = mesh.extents['max']
N = 100
X = numerix.linspace(xmin, xmax, N)
Y = numerix.linspace(ymin, ymax, N)
grid_x, grid_y = numerix.mgrid[xmin:xmax:N * 1j, ymin:ymax:N * 1j]
if isinstance(var, FaceVariable):
C = mesh.faceCenters
elif isinstance(var, CellVariable):
C = mesh.cellCenters
U = griddata(C.value.T, var.value[0], (grid_x, grid_y), method='cubic')
V = griddata(C.value.T, var.value[1], (grid_x, grid_y), method='cubic')
lw = self.linewidth
if isinstance(lw, (FaceVariable, CellVariable)):
lw = griddata(C.value.T,
lw.value, (grid_x, grid_y),
method='cubic')
color = self.color
if isinstance(color, (FaceVariable, CellVariable)):
color = griddata(C.value.T,
color.value, (grid_x, grid_y),
method='cubic',
fill_value=color.min())
U = U.T
V = V.T
ang = numerix.arctan2(V, U)
mag = numerix.sqrt(U**2 + V**2)
datamin, datamax = self._autoscale(vars=(mag, ),
datamin=self._getLimit('datamin'),
datamax=self._getLimit('datamax'))
mag = numerix.where(mag > datamax, numerix.nan, mag)
mag = numerix.where(mag < datamin, numerix.nan, mag)
if self.log:
mag = numerix.log10(mag)
U = mag * numerix.cos(ang)
V = mag * numerix.sin(ang)
# if self._stream is not None:
# # the following doesn't work, nor does it help to `add_collection` first
# # self._stream.arrows.remove()
# self._stream.lines.remove()
self.axes.cla()
self._stream = self.axes.streamplot(X,
Y,
U,
V,
linewidth=lw,
color=color,
**self.kwargs)
self.axes.set_xlim(xmin=self._getLimit('xmin'),
xmax=self._getLimit('xmax'))
self.axes.set_ylim(ymin=self._getLimit('ymin'),
ymax=self._getLimit('ymax'))
def runLeveler(kLeveler=0.018,
bulkLevelerConcentration=0.02,
cellSize=0.1e-7,
rateConstant=0.00026,
initialAcceleratorCoverage=0.0,
levelerDiffusionCoefficient=5e-10,
numberOfSteps=400,
displayRate=10,
displayViewers=True):
kLevelerConsumption = 0.0005
aspectRatio = 1.5
faradaysConstant = 9.6485e4
gasConstant = 8.314
acceleratorDiffusionCoefficient = 4e-10
siteDensity = 6.35e-6
atomicVolume = 7.1e-6
charge = 2
metalDiffusionCoefficient = 4e-10
temperature = 298.
overpotential = -0.25
bulkMetalConcentration = 250.
bulkAcceleratorConcentration = 50.0e-3
initialLevelerCoverage = 0.
cflNumber = 0.2
numberOfCellsInNarrowBand = 20
cellsBelowTrench = 10
trenchDepth = 0.4e-6
trenchSpacing = 0.6e-6
boundaryLayerDepth = 98.7e-6
i0Suppressor = 0.3
i0Accelerator = 22.5
alphaSuppressor = 0.5
alphaAccelerator = 0.4
alphaAdsorption = 0.62
m = 4
b = 2.65
A = 0.3
Ba = -40
Bb = 60
Vd = 0.098
Bd = 0.0008
etaPrime = faradaysConstant * overpotential / gasConstant / temperature
from fipy import TrenchMesh
from fipy.tools import numerix
mesh = TrenchMesh(cellSize=cellSize,
trenchSpacing=trenchSpacing,
trenchDepth=trenchDepth,
boundaryLayerDepth=boundaryLayerDepth,
aspectRatio=aspectRatio,
angle=numerix.pi * 4. / 180.,
bowWidth=0.,
overBumpRadius=0.,
overBumpWidth=0.)
narrowBandWidth = numberOfCellsInNarrowBand * cellSize
from fipy.models.levelSet.distanceFunction.distanceVariable import DistanceVariable
distanceVar = DistanceVariable(name='distance variable',
mesh=mesh,
value=-1,
narrowBandWidth=narrowBandWidth)
distanceVar.setValue(1, where=mesh.getElectrolyteMask())
distanceVar.calcDistanceFunction(narrowBandWidth=1e10)
from fipy.models.levelSet.surfactant.surfactantVariable import SurfactantVariable
levelerVar = SurfactantVariable(name="leveler variable",
value=initialLevelerCoverage,
distanceVar=distanceVar)
acceleratorVar = SurfactantVariable(name="accelerator variable",
value=initialAcceleratorCoverage,
distanceVar=distanceVar)
from fipy.variables.cellVariable import CellVariable
bulkAcceleratorVar = CellVariable(name='bulk accelerator variable',
mesh=mesh,
value=bulkAcceleratorConcentration)
bulkLevelerVar = CellVariable(name='bulk leveler variable',
mesh=mesh,
value=bulkLevelerConcentration)
metalVar = CellVariable(name='metal variable',
mesh=mesh,
value=bulkMetalConcentration)
def depositionCoeff(alpha, i0):
expo = numerix.exp(-alpha * etaPrime)
return 2 * i0 * (expo - expo * numerix.exp(etaPrime))
coeffSuppressor = depositionCoeff(alphaSuppressor, i0Suppressor)
coeffAccelerator = depositionCoeff(alphaAccelerator, i0Accelerator)
exchangeCurrentDensity = acceleratorVar.getInterfaceVar() * (
coeffAccelerator - coeffSuppressor) + coeffSuppressor
currentDensity = metalVar / bulkMetalConcentration * exchangeCurrentDensity
depositionRateVariable = currentDensity * atomicVolume / charge / faradaysConstant
extensionVelocityVariable = CellVariable(name='extension velocity',
mesh=mesh,
value=depositionRateVariable)
from fipy.models.levelSet.surfactant.adsorbingSurfactantEquation \
import AdsorbingSurfactantEquation
kAccelerator = rateConstant * numerix.exp(-alphaAdsorption * etaPrime)
kAcceleratorConsumption = Bd + A / (numerix.exp(Ba *
(overpotential + Vd)) +
numerix.exp(Bb * (overpotential + Vd)))
q = m * overpotential + b
levelerSurfactantEquation = AdsorbingSurfactantEquation(
levelerVar,
distanceVar=distanceVar,
bulkVar=bulkLevelerVar,
rateConstant=kLeveler,
consumptionCoeff=kLevelerConsumption * depositionRateVariable)
accVar1 = acceleratorVar.getInterfaceVar()
accVar2 = (accVar1 > 0) * accVar1
accConsumptionCoeff = kAcceleratorConsumption * (accVar2**(q - 1))
acceleratorSurfactantEquation = AdsorbingSurfactantEquation(
acceleratorVar,
distanceVar=distanceVar,
bulkVar=bulkAcceleratorVar,
rateConstant=kAccelerator,
otherVar=levelerVar,
otherBulkVar=bulkLevelerVar,
otherRateConstant=kLeveler,
consumptionCoeff=accConsumptionCoeff)
from fipy.models.levelSet.advection.higherOrderAdvectionEquation \
import buildHigherOrderAdvectionEquation
advectionEquation = buildHigherOrderAdvectionEquation(
advectionCoeff=extensionVelocityVariable)
from fipy.boundaryConditions.fixedValue import FixedValue
from fipy.models.levelSet.electroChem.metalIonDiffusionEquation \
import buildMetalIonDiffusionEquation
metalEquation = buildMetalIonDiffusionEquation(
ionVar=metalVar,
distanceVar=distanceVar,
depositionRate=depositionRateVariable,
diffusionCoeff=metalDiffusionCoefficient,
metalIonMolarVolume=atomicVolume)
metalEquationBCs = FixedValue(mesh.getTopFaces(), bulkMetalConcentration)
from fipy.models.levelSet.surfactant.surfactantBulkDiffusionEquation \
import buildSurfactantBulkDiffusionEquation
bulkAcceleratorEquation = buildSurfactantBulkDiffusionEquation(
bulkVar=bulkAcceleratorVar,
distanceVar=distanceVar,
surfactantVar=acceleratorVar,
otherSurfactantVar=levelerVar,
diffusionCoeff=acceleratorDiffusionCoefficient,
rateConstant=kAccelerator * siteDensity)
bulkAcceleratorEquationBCs = (FixedValue(mesh.getTopFaces(),
bulkAcceleratorConcentration), )
bulkLevelerEquation = buildSurfactantBulkDiffusionEquation(
bulkVar=bulkLevelerVar,
distanceVar=distanceVar,
surfactantVar=levelerVar,
diffusionCoeff=levelerDiffusionCoefficient,
rateConstant=kLeveler * siteDensity)
bulkLevelerEquationBCs = (FixedValue(mesh.getTopFaces(),
bulkLevelerConcentration), )
eqnTuple = ((advectionEquation, distanceVar,
()), (levelerSurfactantEquation, levelerVar,
()), (acceleratorSurfactantEquation, acceleratorVar,
()), (metalEquation, metalVar, metalEquationBCs),
(bulkAcceleratorEquation, bulkAcceleratorVar,
bulkAcceleratorEquationBCs),
(bulkLevelerEquation, bulkLevelerVar, bulkLevelerEquationBCs))
levelSetUpdateFrequency = int(0.7 * narrowBandWidth / cellSize /
cflNumber / 2)
totalTime = 0.0
if displayViewers:
from fipy.viewers.mayaviViewer.mayaviSurfactantViewer import MayaviSurfactantViewer
viewers = (MayaviSurfactantViewer(distanceVar,
acceleratorVar.getInterfaceVar(),
zoomFactor=1e6,
limits={
'datamax': 0.5,
'datamin': 0.0
},
smooth=1,
title='accelerator coverage'),
MayaviSurfactantViewer(distanceVar,
levelerVar.getInterfaceVar(),
zoomFactor=1e6,
limits={
'datamax': 0.5,
'datamin': 0.0
},
smooth=1,
title='leveler coverage'))
for step in range(numberOfSteps):
if displayViewers:
if step % displayRate == 0:
for viewer in viewers:
viewer.plot()
if step % levelSetUpdateFrequency == 0:
distanceVar.calcDistanceFunction(deleteIslands=True)
extensionVelocityVariable.setValue(depositionRateVariable)
extOnInt = numerix.where(
distanceVar > 0,
numerix.where(distanceVar < 2 * cellSize,
extensionVelocityVariable, 0), 0)
dt = cflNumber * cellSize / numerix.max(extOnInt)
id = numerix.max(numerix.nonzero(distanceVar._getInterfaceFlag()))
distanceVar.extendVariable(extensionVelocityVariable,
deleteIslands=True)
extensionVelocityVariable[mesh.getFineMesh().getNumberOfCells():] = 0.
for eqn, var, BCs in eqnTuple:
var.updateOld()
for eqn, var, BCs in eqnTuple:
eqn.solve(var, boundaryConditions=BCs, dt=dt)
totalTime += dt
try:
testFile = 'testLeveler.gz'
import os
import examples.levelSet.electroChem
from fipy.tools import dump
data = dump.read(
os.path.join(examples.levelSet.electroChem.__path__[0], testFile))
N = mesh.getFineMesh().getNumberOfCells()
print numerix.allclose(data[:N], levelerVar[:N], rtol=1e-3)
except:
return 0
def _getStructure(self):
##maxX = self.distanceVar.mesh.faceCenters[0].max()
##minX = self.distanceVar.mesh.faceCenters[0].min()
IDs = numerix.nonzero(self.distanceVar._cellInterfaceFlag)[0]
coordinates = numerix.take(numerix.array(self.distanceVar.mesh.cellCenters).swapaxes(0, 1), IDs)
coordinates -= numerix.take(numerix.array(self.distanceVar.grad * self.distanceVar).swapaxes(0, 1), IDs)
coordinates *= self.zoomFactor
shiftedCoords = coordinates.copy()
shiftedCoords[:, 0] = -coordinates[:, 0] ##+ (maxX - minX)
coordinates = numerix.concatenate((coordinates, shiftedCoords))
from .lines import _getOrderedLines
lines = _getOrderedLines(list(range(2 * len(IDs))), coordinates, thresholdDistance = self.distanceVar.mesh._cellDistances.min() * 10)
data = numerix.take(self.surfactantVar, IDs)
data = numerix.concatenate((data, data))
tmpIDs = numerix.nonzero(data > 0.0001)[0]
if len(tmpIDs) > 0:
val = numerix.take(data, tmpIDs).min()
else:
val = 0.0001
data = numerix.where(data < 0.0001,
val,
data)
for line in lines:
if len(line) > 2:
for smooth in range(self.smooth):
for arr in (coordinates, data):
tmp = numerix.take(arr, line)
tmp[1:-1] = tmp[2:] * 0.25 + tmp[:-2] * 0.25 + tmp[1:-1] * 0.5
if len(arr.shape) > 1:
for i in range(len(arr[0])):
arrI = arr[:, i].copy()
numerix.put(arrI, line, tmp[:, i])
arr[:, i] = arrI
else:
numerix.put(arrI, line, tmp)
name = self.title
name = name.strip()
if name == '':
name = None
coords = numerix.zeros((coordinates.shape[0], 3), 'd')
coords[:, :coordinates.shape[1]] = coordinates
import pyvtk
## making lists as pyvtk doesn't know what to do with numpy arrays
coords = list(coords)
coords = [[float(coord[0]), float(coord[1]), float(coord[2])] for coord in coords]
data = list(data)
data = [float(item) for item in data]
return (pyvtk.UnstructuredGrid(points = coords,
poly_line = lines),
pyvtk.PointData(pyvtk.Scalars(data, name = name)))
def logs_to_signed(v, plus, minus):
v = numerix.where(v > 0, plus, -minus)
v = numerix.where(numerix.isnan(v), 0., v)
return v
def signed_to_logs(v):
return (numerix.where(v > 0, numerix.log10(v), numerix.nan),
numerix.where(v < 0, numerix.log10(-v), numerix.nan))
def _calcValue(self):
P = self.P.numericValue
alpha = numerix.where(P > 0., 1., 0.)
return PhysicalField(value=alpha)
nx = 50
valueLeft = 0.
fluxRight = 1.
timeStepDuration = 1.
L = 1.
dx = L / nx
mesh = Grid1D(dx = dx, nx = nx)
var = CellVariable(
name = "solution variable",
mesh = mesh,
value = valueLeft)
x = mesh.getFaceCenters()[:,0]
middleFaces = numerix.logical_or(x < L / 4.,x >= 3. * L / 4.)
diffCoeff = numerix.where(middleFaces, 1., 0.1)
boundaryConditions=(FixedValue(mesh.getFacesLeft(),valueLeft),
FixedFlux(mesh.getFacesRight(),fluxRight))
if __name__ == '__main__':
import fipy.viewers
viewer = fipy.viewers.make(vars = var, limits = {'datamax': L + 18. * L / 4.})
viewer.plot()
raw_input('finished')
def _calcValue(self):
areas = numerix.array(
self.surfactantVar.distanceVar.cellInterfaceAreas)
areas = numerix.where(areas > 1e-20, areas, 1)
return numerix.array(
self.surfactantVar) * self.mesh.cellVolumes / areas
def _calcValue(self):
P = self.P.numericValue
alpha = numerix.where(P > 0., 1., 0.)
return PhysicalField(value=alpha)
