def __init__(self, coeff):
"""
.. attention:: This class is deprecated. Use `ExplicitDiffusionTerm` instead.
"""
import warnings
warnings.warn("ExplicitDiffusionTerm should be used instead of ExplicitNthOrderDiffusionTerm", DeprecationWarning, stacklevel=2)
ExplicitDiffusionTerm.__init__(self, coeff = coeff)
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
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')
#Laplacian=0
nx = 50
dx = 1.
from fipy.meshes.grid1D import Grid1D
mesh = Grid1D(nx=nx, dx=dx)
from fipy.variables.cellVariable import CellVariable
phi = CellVariable(name="solution variable", mesh=mesh, value=0)
z = CellVariable(name="dummy", mesh=mesh, value=0)
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
eqX = ExplicitDiffusionTerm(coeff=1)
from fipy import viewers
viewer = viewers.make(vars=(phi), limits={'datamin': 0., 'datamax': 1.})
viewer.plot()
eqX.solve(var=phi, boundaryConditions=BCs)
viewer.plot()
phi = CellVariable(name="solution variable",
mesh=mesh,
value=0)
z = CellVariable(name="dummy",
mesh=mesh,
value=0)
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
eqX = ExplicitDiffusionTerm(coeff=1)
from fipy import viewers
viewer = viewers.make(vars=(phi),
limits={'datamin': 0., 'datamax': 1.})
viewer.plot()
eqX.solve(var=phi,
boundaryConditions=BCs)
viewer.plot()
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()
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)
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,