def buildPhaseEquation(phase, theta):
mPhiVar = phase - 0.5 + temperature * phase * (1 - phase)
thetaMag = theta.getOld().getGrad().getMag()
implicitSource = mPhiVar * (phase - (mPhiVar < 0))
implicitSource += (2 * s + epsilon**2 * thetaMag) * thetaMag
return TransientTerm(phaseTransientCoeff) == \
ExplicitDiffusionTerm(alpha**2) \
- ImplicitSourceTerm(implicitSource) \
+ (mPhiVar > 0) * mPhiVar * phase
def buildThetaEquation(phase, theta):
phaseMod = phase + (phase < thetaSmallValue) * thetaSmallValue
phaseModSq = phaseMod * phaseMod
expo = epsilon * beta * theta.getGrad().getMag()
expo = (expo < 100.) * (expo - 100.) + 100.
pFunc = 1. + numerix.exp(-expo) * (mu / epsilon - 1.)
phaseFace = phase.getArithmeticFaceValue()
phaseSq = phaseFace * phaseFace
gradMag = theta.getFaceGrad().getMag()
eps = 1. / gamma / 10.
gradMag += (gradMag < eps) * eps
IGamma = (gradMag > 1. / gamma) * (1 / gradMag - gamma) + gamma
diffusionCoeff = phaseSq * (s * IGamma + epsilon**2)
thetaGradDiff = theta.getFaceGrad() - theta.getFaceGradNoMod()
sourceCoeff = (diffusionCoeff * thetaGradDiff).getDivergence()
from fipy.terms.implicitDiffusionTerm import ImplicitDiffusionTerm
return TransientTerm(thetaTransientCoeff * phaseModSq * pFunc) == \
ImplicitDiffusionTerm(diffusionCoeff) \
+ sourceCoeff
steps = 1000
mesh = Grid1D(dx=dx, nx=nx)
startingArray = numerix.zeros(nx, 'd')
startingArray[50:90] = 1.
var = CellVariable(name="advection variable", mesh=mesh, value=startingArray)
boundaryConditions = (FixedValue(mesh.getFacesLeft(), valueLeft),
FixedValue(mesh.getFacesRight(), valueRight))
from fipy.terms.transientTerm import TransientTerm
from fipy.terms.powerLawConvectionTerm import PowerLawConvectionTerm
eq = TransientTerm() - PowerLawConvectionTerm(coeff=(velocity, ))
if __name__ == '__main__':
viewer = fipy.viewers.make(vars=(var, ))
viewer.plot()
raw_input("press key to continue")
for step in range(steps):
eq.solve(var,
dt=timeStepDuration,
boundaryConditions=boundaryConditions,
solver=LinearLUSolver(tolerance=1.e-15))
viewer.plot()
viewer.plot()
raw_input('finished')
def buildMetalIonDiffusionEquation(ionVar=None,
distanceVar=None,
depositionRate=1,
transientCoeff=1,
diffusionCoeff=1,
metalIonMolarVolume=1):
r"""
The `MetalIonDiffusionEquation` solves the diffusion of the metal
species with a source term at the electrolyte interface. The governing
equation is given by,
.. math::
\frac{\partial c}{\partial t} = \nabla \cdot D \nabla c
where,
.. math::
D = \begin{cases}
D_c & \text{when $\phi > 0$} \\
0 & \text{when $\phi \le 0$}
\end{cases}
The velocity of the interface generally has a linear dependence on ion
concentration. The following boundary condition applies at the zero
level set,
.. math::
D \hat{n} \cdot \nabla c = \frac{v(c)}{\Omega} \qquad \text{at $phi = 0$}
where
.. math::
v(c) = c V_0
The test case below is for a 1D steady state problem. The solution is
given by:
.. math::
c(x) = \frac{c^{\infty}}{\Omega D / V_0 + L}\left(x - L\right) + c^{\infty}
This is the test case,
>>> from fipy.meshes import Grid1D
>>> nx = 11
>>> dx = 1.
>>> from fipy.tools import serialComm
>>> mesh = Grid1D(nx = nx, dx = dx, communicator=serialComm)
>>> x, = mesh.cellCenters
>>> from fipy.variables.cellVariable import CellVariable
>>> ionVar = CellVariable(mesh = mesh, value = 1.)
>>> from fipy.variables.distanceVariable \
... import DistanceVariable
>>> disVar = DistanceVariable(mesh = mesh,
... value = (x - 0.5) - 0.99,
... hasOld = 1)
>>> v = 1.
>>> diffusion = 1.
>>> omega = 1.
>>> cinf = 1.
>>> eqn = buildMetalIonDiffusionEquation(ionVar = ionVar,
... distanceVar = disVar,
... depositionRate = v * ionVar,
... diffusionCoeff = diffusion,
... metalIonMolarVolume = omega)
>>> ionVar.constrain(cinf, mesh.facesRight)
>>> from builtins import range
>>> for i in range(10):
... eqn.solve(ionVar, dt = 1000)
>>> L = (nx - 1) * dx - dx / 2
>>> gradient = cinf / (omega * diffusion / v + L)
>>> answer = gradient * (x - L - dx * 3 / 2) + cinf
>>> answer[x < dx] = 1
>>> print(ionVar.allclose(answer))
1
Testing the interface source term
>>> from fipy.meshes import Grid2D
>>> from fipy import numerix, serialComm
>>> mesh = Grid2D(dx = 1., dy = 1., nx = 2, ny = 2, communicator=serialComm)
>>> from fipy.variables.distanceVariable import DistanceVariable
>>> distance = DistanceVariable(mesh = mesh, value = (-.5, .5, .5, 1.5))
>>> ionVar = CellVariable(mesh = mesh, value = (1, 1, 1, 1))
>>> depositionRate = CellVariable(mesh=mesh, value=(1, 1, 1, 1))
>>> source = depositionRate * distance.cellInterfaceAreas / mesh.cellVolumes / ionVar
>>> sqrt = numerix.sqrt(2)
>>> ans = CellVariable(mesh=mesh, value=(0, 1 / sqrt, 1 / sqrt, 0))
>>> print(numerix.allclose(source, ans))
True
>>> distance[:] = (-1.5, -0.5, -0.5, 0.5)
>>> print(numerix.allclose(source, (0, 0, 0, sqrt)))
True
:Parameters:
- `ionVar`: The metal ion concentration variable.
- `distanceVar`: A `DistanceVariable` object.
- `depositionRate`: A float or a `CellVariable` representing the interface deposition rate.
- `transientCoeff`: The transient coefficient.
- `diffusionCoeff`: The diffusion coefficient
- `metalIonMolarVolume`: Molar volume of the metal ions.
"""
diffusionCoeff = _LevelSetDiffusionVariable(distanceVar, diffusionCoeff)
eq = TransientTerm(transientCoeff) - DiffusionTermNoCorrection(
diffusionCoeff)
mesh = distanceVar.mesh
coeff = depositionRate * distanceVar.cellInterfaceAreas / (
mesh.cellVolumes * metalIonMolarVolume) / ionVar
return eq + ImplicitSourceTerm(coeff)
startingArray = numerix.zeros(nx, 'd')
startingArray[50:90] = 1.
var = CellVariable(
name = "advection variable",
mesh = mesh,
value = startingArray)
boundaryConditions = (
FixedValue(mesh.getFacesLeft(), valueLeft),
FixedValue(mesh.getFacesRight(), valueRight)
)
from fipy.terms.transientTerm import TransientTerm
from fipy.terms.explicitUpwindConvectionTerm import ExplicitUpwindConvectionTerm
eq = TransientTerm() - ExplicitUpwindConvectionTerm(coeff = (velocity,))
if __name__ == '__main__':
viewer = fipy.viewers.make(vars=(var,))
for step in range(steps):
eq.solve(var,
dt = timeStepDuration,
boundaryConditions = boundaryConditions,
solver = LinearCGSSolver(tolerance = 1.e-15, steps = 2000))
viewer.plot()
viewer.plot()
raw_input('finished')
def buildSurfactantBulkDiffusionEquation(bulkVar=None,
distanceVar=None,
surfactantVar=None,
otherSurfactantVar=None,
diffusionCoeff=None,
transientCoeff=1.,
rateConstant=None):
r"""
The `buildSurfactantBulkDiffusionEquation` function returns a bulk diffusion of a
species with a source term for the jump from the bulk to an interface.
The governing equation is given by,
.. math::
\frac{\partial c}{\partial t} = \nabla \cdot D \nabla c
where,
.. math::
D = \begin{cases}
D_c & \text{when $\phi > 0$} \\
0 & \text{when $\phi \le 0$}
\end{cases}
The jump condition at the interface is defined by Langmuir
adsorption. Langmuir adsorption essentially states that the ability for
a species to jump from an electrolyte to an interface is proportional to
the concentration in the electrolyte, available site density and a
jump coefficient. The boundary condition at the interface is given by
.. math::
D \hat{n} \cdot \nabla c = -k c (1 - \theta) \qquad \text{at $\phi = 0$}.
Parameters
----------
bulkVar : ~fipy.variables.cellVariable.CellVariable
The bulk surfactant concentration variable.
distanceVar : ~fipy.variables.distanceVariable.DistanceVariable
surfactantVar : ~fipy.variables.surfactantVariable.SurfactantVariable
otherSurfactantVar : ~fipy.variables.surfactantVariable.SurfactantVariable
Any other surfactants that may remove this one.
diffusionCoeff : float or ~fipy.variables.faceVariable.FaceVariable
transientCoeff : float
In general 1 is used.
rateConstant : float
The adsorption coefficient.
"""
spCoeff = rateConstant * distanceVar.cellInterfaceAreas / bulkVar.mesh.cellVolumes
spSourceTerm = ImplicitSourceTerm(spCoeff)
bulkSpCoeff = spCoeff * bulkVar
coeff = bulkSpCoeff * surfactantVar.interfaceVar
diffusionCoeff = _LevelSetDiffusionVariable(distanceVar, diffusionCoeff)
eq = TransientTerm(transientCoeff) - DiffusionTermNoCorrection(
diffusionCoeff)
if otherSurfactantVar is not None:
otherCoeff = bulkSpCoeff * otherSurfactantVar.interfaceVar
else:
otherCoeff = 0
return eq - coeff + spSourceTerm - otherCoeff
from fipy.meshes.periodicGrid1D import PeriodicGrid1D
periodicMesh = PeriodicGrid1D(dx=dx, nx=nx / 2)
startingArray = numerix.zeros(nx, 'd')
startingArray[2 * nx / 10:3 * nx / 10] = 1.
from fipy.variables.cellVariable import CellVariable
var1 = CellVariable(name="non-periodic", mesh=mesh, value=startingArray)
var2 = CellVariable(name="periodic",
mesh=periodicMesh,
value=startingArray[:nx / 2])
from fipy.terms.transientTerm import TransientTerm
from fipy.terms.vanLeerConvectionTerm import VanLeerConvectionTerm
eq1 = TransientTerm() - VanLeerConvectionTerm(coeff=(-velocity, ))
eq2 = TransientTerm() - VanLeerConvectionTerm(coeff=(-velocity, ))
if __name__ == '__main__':
import fipy.viewers
viewer1 = fipy.viewers.make(vars=var1)
viewer2 = fipy.viewers.make(vars=var2)
viewer1.plot()
viewer2.plot()
from fipy.solvers.linearLUSolver import LinearLUSolver
newVar2 = var2.copy()
for step in range(steps):
eq1.solve(var=var1, dt=dt, solver=LinearLUSolver())
mesh = Grid1D(nx=nx, dx=dx)
from fipy.variables.cellVariable import CellVariable
phi = CellVariable(name="solution variable", mesh=mesh, value=0)
D = 1
valueLeft = 1
valueRight = 0
from fipy.boundaryConditions.fixedValue import FixedValue
BCs = (FixedValue(faces=mesh.getFacesRight(), value=valueRight),
FixedValue(faces=mesh.getFacesLeft(), value=valueLeft))
from fipy.terms.explicitDiffusionTerm import ExplicitDiffusionTerm
from fipy.terms.transientTerm import TransientTerm
eqX = TransientTerm() == ExplicitDiffusionTerm(coeff=D)
timeStepDuration = 0.9 * dx**2 / (2 * D)
steps = 100
from fipy import viewers
viewer = viewers.make(vars=(phi), limits={'datamin': 0., 'datamax': 1.})
def hit_continue(Prompt='Hit any key to continue'):
raw_input(Prompt)
for step in range(steps):
eqX.solve(var=phi, boundaryConditions=BCs, dt=timeStepDuration)
viewer.plot()
shift = 1. KMVar = CellVariable(mesh = mesh, value = params['KM'] * shift, hasOld = 1) KCVar = CellVariable(mesh = mesh, value = params['KC'] * shift, hasOld = 1) TMVar = CellVariable(mesh = mesh, value = params['TM'] * shift, hasOld = 1) TCVar = CellVariable(mesh = mesh, value = params['TC'] * shift, hasOld = 1) P3Var = CellVariable(mesh = mesh, value = params['P3'] * shift, hasOld = 1) P2Var = CellVariable(mesh = mesh, value = params['P2'] * shift, hasOld = 1) RVar = CellVariable(mesh = mesh, value = params['R'], hasOld = 1) PN = P3Var + P2Var KMscCoeff = params['chiK'] * (RVar + 1) * (1 - KCVar - KMVar.getCellVolumeAverage()) KMspCoeff = params['lambdaK'] / (1 + PN / params['kappaK']) KMEq = TransientTerm() - KMscCoeff + ImplicitSourceTerm(KMspCoeff) TMscCoeff = params['chiT'] * (1 - TCVar - TMVar.getCellVolumeAverage()) TMspCoeff = params['lambdaT'] * (KMVar + params['zetaT']) TMEq = TransientTerm() - TMscCoeff + ImplicitSourceTerm(TMspCoeff) TCscCoeff = params['lambdaT'] * (TMVar * KMVar).getCellVolumeAverage() TCspCoeff = params['lambdaTstar'] TCEq = TransientTerm() - TCscCoeff + ImplicitSourceTerm(TCspCoeff) PIP2PITP = PN / (PN / params['kappam'] + PN.getCellVolumeAverage() / params['kappac'] + 1) + params['zetaPITP'] P3spCoeff = params['lambda3'] * (TMVar + params['zeta3T']) P3scCoeff = params['chi3'] * KMVar * (PIP2PITP / (1 + KMVar / params['kappa3']) + params['zeta3PITP']) + params['zeta3'] P3Eq = TransientTerm() - ImplicitDiffusionTerm(params['diffusionCoeff']) - P3scCoeff + ImplicitSourceTerm(P3spCoeff)
mesh = Grid2D(dx, dy, nx, ny)
from fipy.variables.cellVariable import CellVariable
from fipy.tools.numerix import random
var = CellVariable(name="phase field", mesh=mesh, value=random.random(nx * ny))
faceVar = var.getArithmeticFaceValue()
doubleWellDerivative = asq * (1 - 6 * faceVar * (1 - faceVar))
from fipy.terms.implicitDiffusionTerm import ImplicitDiffusionTerm
from fipy.terms.transientTerm import TransientTerm
diffTerm2 = ImplicitDiffusionTerm(coeff=(diffusionCoeff *
doubleWellDerivative, ))
diffTerm4 = ImplicitDiffusionTerm(coeff=(diffusionCoeff, -epsilon**2))
eqch = TransientTerm() - diffTerm2 - diffTerm4
from fipy.solvers.linearPCGSolver import LinearPCGSolver
from fipy.solvers.linearLUSolver import LinearLUSolver
##solver = LinearLUSolver(tolerance = 1e-15,steps = 1000)
solver = LinearPCGSolver(tolerance=1e-15, steps=1000)
from fipy.boundaryConditions.fixedValue import FixedValue
from fipy.boundaryConditions.fixedFlux import FixedFlux
from fipy.boundaryConditions.nthOrderBoundaryCondition import NthOrderBoundaryCondition
BCs = (FixedFlux(mesh.getFacesRight(), 0), FixedFlux(mesh.getFacesLeft(), 0),
NthOrderBoundaryCondition(mesh.getFacesLeft(), 0, 3),
NthOrderBoundaryCondition(mesh.getFacesRight(), 0, 3),
NthOrderBoundaryCondition(mesh.getFacesTop(), 0, 3),
NthOrderBoundaryCondition(mesh.getFacesBottom(), 0, 3))
def __init__(self,
surfactantVar=None,
distanceVar=None,
bulkVar=None,
rateConstant=None,
otherVar=None,
otherBulkVar=None,
otherRateConstant=None,
consumptionCoeff=None):
"""
Create a `AdsorbingSurfactantEquation` object.
:Parameters:
- `surfactantVar`: The `SurfactantVariable` to be solved for.
- `distanceVar`: The `DistanceVariable` that marks the interface.
- `bulkVar`: The value of the `surfactantVar` in the bulk.
- `rateConstant`: The adsorption rate of the `surfactantVar`.
- `otherVar`: Another `SurfactantVariable` with more surface affinity.
- `otherBulkVar`: The value of the `otherVar` in the bulk.
- `otherRateConstant`: The adsorption rate of the `otherVar`.
- `consumptionCoeff`: The rate that the `surfactantVar` is consumed during deposition.
"""
self.eq = TransientTerm(coeff=1) - ExplicitUpwindConvectionTerm(
SurfactantConvectionVariable(distanceVar))
self.dt = Variable(0.)
mesh = distanceVar.mesh
adsorptionCoeff = self.dt * bulkVar * rateConstant
spCoeff = adsorptionCoeff * distanceVar._cellInterfaceFlag
scCoeff = adsorptionCoeff * distanceVar.cellInterfaceAreas / mesh.cellVolumes
self.eq += ImplicitSourceTerm(spCoeff) - scCoeff
if otherVar is not None:
otherSpCoeff = self.dt * otherBulkVar * otherRateConstant * distanceVar._cellInterfaceFlag
otherScCoeff = -otherVar.interfaceVar * scCoeff
self.eq += ImplicitSourceTerm(otherSpCoeff) - otherScCoeff
vars = (surfactantVar, otherVar)
else:
vars = (surfactantVar, )
total = 0
for var in vars:
total += var.interfaceVar
maxVar = (total > 1) * distanceVar._cellInterfaceFlag
val = distanceVar.cellInterfaceAreas / mesh.cellVolumes
for var in vars[1:]:
val -= distanceVar._cellInterfaceFlag * var
spMaxCoeff = 1e20 * maxVar
scMaxCoeff = spMaxCoeff * val * (val > 0)
self.eq += ImplicitSourceTerm(spMaxCoeff) - scMaxCoeff - 1e-40
if consumptionCoeff is not None:
self.eq += ImplicitSourceTerm(consumptionCoeff)
else:
return 0
def allOthers(face):
if ((leftSide(face) or inMiddle(face) or rightSide(face))
or not (face.getID() in bigMesh.getExteriorFaces())):
return 0
else:
return 1
var = CellVariable(name="concentration", mesh=bigMesh, value=valueLeft)
eqn = TransientTerm() == ExplicitDiffusionTerm()
exteriorFaces = bigMesh.getExteriorFaces()
xFace = exteriorFaces.getCenters()[..., 0]
boundaryConditions = (
FixedValue(exteriorFaces.where(xFace**2 < 0.000000000000001), valueLeft),
FixedValue(exteriorFaces.where((xFace - (dx * nx))**2 < 0.000000000000001),
(valueLeft + valueRight) * 0.5),
FixedValue(
exteriorFaces.where((xFace - (2 * dx * nx))**2 < 0.000000000000001),
valueRight))
answer = numerix.array([
0.00000000e+00, 8.78906250e-23, 1.54057617e-19, 1.19644866e-16,
5.39556276e-14, 1.55308505e-11, 2.94461712e-09, 3.63798469e-07,
# create a field variable, set the initial conditions:
from fipy.variables.cellVariable import CellVariable
var = CellVariable(mesh=mesh, value=0)
def centerCells(cell):
return abs(cell.getCenter()[0] - L / 2.0) < L / 10
var.setValue(value=1.0, cells=mesh.getCells(filter=centerCells))
# create the equation:
from fipy.terms.transientTerm import TransientTerm
from fipy.terms.implicitDiffusionTerm import ImplicitDiffusionTerm
eq = TransientTerm() - ImplicitDiffusionTerm(coeff=1) == 0
# create a viewer:
from fipy.viewers.gist2DViewer import Gist1DViewer
viewer = Gist1DViewer(vars=(var,), limits=('e', 'e', 0, 1))
viwer.plot()
# solve
for i in range(steps):
var.updateOld()
eq.solve()
viewer.plot()
shift = 1.
KMVar = CellVariable(mesh=mesh, value=params['KM'] * shift, hasOld=1)
KCVar = CellVariable(mesh=mesh, value=params['KC'] * shift, hasOld=1)
TMVar = CellVariable(mesh=mesh, value=params['TM'] * shift, hasOld=1)
TCVar = CellVariable(mesh=mesh, value=params['TC'] * shift, hasOld=1)
P3Var = CellVariable(mesh=mesh, value=params['P3'] * shift, hasOld=1)
P2Var = CellVariable(mesh=mesh, value=params['P2'] * shift, hasOld=1)
RVar = CellVariable(mesh=mesh, value=params['R'], hasOld=1)
PN = P3Var + P2Var
KMscCoeff = params['chiK'] * (RVar + 1) * (1 - KCVar -
KMVar.getCellVolumeAverage())
KMspCoeff = params['lambdaK'] / (1 + PN / params['kappaK'])
KMEq = TransientTerm() - KMscCoeff + ImplicitSourceTerm(KMspCoeff)
TMscCoeff = params['chiT'] * (1 - TCVar - TMVar.getCellVolumeAverage())
TMspCoeff = params['lambdaT'] * (KMVar + params['zetaT'])
TMEq = TransientTerm() - TMscCoeff + ImplicitSourceTerm(TMspCoeff)
TCscCoeff = params['lambdaT'] * (TMVar * KMVar).getCellVolumeAverage()
TCspCoeff = params['lambdaTstar']
TCEq = TransientTerm() - TCscCoeff + ImplicitSourceTerm(TCspCoeff)
PIP2PITP = PN / (PN / params['kappam'] + PN.getCellVolumeAverage() /
params['kappac'] + 1) + params['zetaPITP']
P3spCoeff = params['lambda3'] * (TMVar + params['zeta3T'])
P3scCoeff = params['chi3'] * KMVar * (PIP2PITP /
(1 + KMVar / params['kappa3']) +
phaseY = phase.getFaceGrad().dot((0, 1))
phaseX = phase.getFaceGrad().dot((1, 0))
psi = theta + numerix.arctan2(phaseY, phaseX)
Phi = numerix.tan(N * psi / 2)
PhiSq = Phi**2
beta = (1. - PhiSq) / (1. + PhiSq)
betaPsi = -N * 2 * Phi / (1 + PhiSq)
A = alpha**2 * c * (1. + c * beta) * betaPsi
D = alpha**2 * (1. + c * beta)**2
dxi = phase.getFaceGrad()._take((1, 0), axis=1) * (-1, 1)
anisotropySource = (A * dxi).getDivergence()
from fipy.terms.transientTerm import TransientTerm
from fipy.terms.explicitDiffusionTerm import ExplicitDiffusionTerm
from fipy.terms.implicitSourceTerm import ImplicitSourceTerm
phaseEq = TransientTerm(tau) == ExplicitDiffusionTerm(D) + \
ImplicitSourceTerm(mVar * ((mVar < 0) - phase)) + \
((mVar > 0.) * mVar * phase + anisotropySource)
from fipy.terms.implicitDiffusionTerm import ImplicitDiffusionTerm
temperatureEq = TransientTerm() == \
ImplicitDiffusionTerm(tempDiffusionCoeff) + \
(phase - phase.getOld()) / timeStepDuration
bench.stop('terms')
phase.updateOld()
temperature.updateOld()
phaseEq.solve(phase, dt=timeStepDuration)
temperatureEq.solve(temperature, dt=timeStepDuration)
phase = CellVariable(name='PhaseField', mesh=mesh, value=1.)
from fipy.variables.modularVariable import ModularVariable
theta = ModularVariable(name='Theta', mesh=mesh, value=1.)
theta.setValue(0., where=mesh.getCellCenters()[..., 0] > L / 2.)
from fipy.terms.implicitSourceTerm import ImplicitSourceTerm
mPhiVar = phase - 0.5 + temperature * phase * (1 - phase)
thetaMag = theta.getOld().getGrad().getMag()
implicitSource = mPhiVar * (phase - (mPhiVar < 0))
implicitSource += (2 * s + epsilon**2 * thetaMag) * thetaMag
from fipy.terms.transientTerm import TransientTerm
from fipy.terms.explicitDiffusionTerm import ExplicitDiffusionTerm
phaseEq = TransientTerm(phaseTransientCoeff) == \
ExplicitDiffusionTerm(alpha**2) \
- ImplicitSourceTerm(implicitSource) \
+ (mPhiVar > 0) * mPhiVar * phase
if __name__ == '__main__':
import fipy.viewers
phaseViewer = fipy.viewers.make(vars=phase)
phaseViewer.plot()
for step in range(steps):
phaseEq.solve(phase, dt=timeStepDuration)
phaseViewer.plot()
raw_input('finished')
bench.start()
from fipy.variables.cellVariable import CellVariable
C = CellVariable(mesh=mesh)
C.setValue(1, where=abs(mesh.getCellCenters()[..., 0] - L / 2.) < L / 10.)
bench.stop('variables')
bench.start()
D = 1.
from fipy.terms.implicitDiffusionTerm import ImplicitDiffusionTerm
from fipy.terms.transientTerm import TransientTerm
eq = TransientTerm() == ImplicitDiffusionTerm(coeff=D)
bench.stop('terms')
## from fipy import viewers
## viewer = viewers.make(vars = C, limits = {'datamin': 0, 'datamax': 1})
## viewer.plot()
## raw_input("initial")
bench.start()
dt = 1e0
steps = 1
for step in range(steps):
eq.solve(var=C, dt=dt)
## viewer.plot()
