alpha = 0.015
temperature = 1.
dx = L / nx
from fipy.meshes.grid1D import Grid1D
mesh = Grid1D(dx=dx, nx=nx)
from fipy.variables.cellVariable import CellVariable
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
temperature = 10.
bench.start()
from fipy.variables.cellVariable import CellVariable
phase = CellVariable(
name = 'PhaseField',
mesh = mesh,
value = 0.
)
from fipy.variables.modularVariable import ModularVariable
pi = numerix.pi
theta = ModularVariable(
name = 'Theta',
mesh = mesh,
value = -pi + 0.0001,
hasOld = 1
)
x, y = mesh.getCellCenters()[...,0], mesh.getCellCenters()[...,1]
for a, b, thetaValue in ((0., 0., 2. * pi / 3.),
(Lx, 0., -2. * pi / 3.),
(0., Lx, -2. * pi / 3. + 0.3),
(Lx, Lx, 2. * pi / 3.)):
segment = (x - a)**2 + (y - b)**2 < (Lx / 2.)**2
phase.setValue(1., where=segment)
theta.setValue(thetaValue, where=segment)
bench.stop('variables')
bench.start()
thetaTransientCoeff = 0.01
gamma = 1e3
epsilon = 0.008
s = 0.01
alpha = 0.015
temperature = 10.
bench.start()
from fipy.variables.cellVariable import CellVariable
phase = CellVariable(name='PhaseField', mesh=mesh, value=0.)
from fipy.variables.modularVariable import ModularVariable
pi = numerix.pi
theta = ModularVariable(name='Theta',
mesh=mesh,
value=-pi + 0.0001,
hasOld=1)
x, y = mesh.getCellCenters()[..., 0], mesh.getCellCenters()[..., 1]
for a, b, thetaValue in ((0., 0., 2. * pi / 3.), (Lx, 0., -2. * pi / 3.),
(0., Lx, -2. * pi / 3. + 0.3), (Lx, Lx,
2. * pi / 3.)):
segment = (x - a)**2 + (y - b)**2 < (Lx / 2.)**2
phase.setValue(1., where=segment)
theta.setValue(thetaValue, where=segment)
bench.stop('variables')
bench.start()
from fipy.terms.transientTerm import TransientTerm
phaseTransientCoeff = 0.1
epsilon = 0.008
s = 0.01
alpha = 0.015
dx = L / nx
dy = L / ny
from fipy.meshes.grid2D import Grid2D
mesh = Grid2D(dx, dy, nx, ny)
from fipy.variables.cellVariable import CellVariable
phase = CellVariable(name = 'PhaseField', mesh = mesh, value = 1.)
from fipy.variables.modularVariable import ModularVariable
theta = ModularVariable(name = 'Theta', mesh = mesh, value = 1.)
x, y = mesh.getCellCenters()[...,0], mesh.getCellCenters()[...,1]
theta.setValue(0., where=(x - L / 2.)**2 + (y - L / 2.)**2 < (L / 4.)**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
epsilon = 0.008
s = 0.01
alpha = 0.015
dx = L / nx
dy = L / ny
from fipy.meshes.grid2D import Grid2D
mesh = Grid2D(dx, dy, nx, ny)
from fipy.variables.cellVariable import CellVariable
phase = CellVariable(name = 'PhaseField', mesh = mesh, value = 1.)
from fipy.variables.modularVariable import ModularVariable
from fipy.tools import numerix
theta = ModularVariable(name = 'Theta', mesh = mesh, value = 2. * numerix.pi / 3.)
x, y = mesh.getCellCenters()[...,0], mesh.getCellCenters()[...,1]
theta.setValue(-2. * numerix.pi / 3., where=(x - L / 2.)**2 + (y - L / 2.)**2 < (L / 4.)**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
phaseTransientCoeff = 0.1
epsilon = 0.008
s = 0.01
alpha = 0.015
temperature = 1.
dx = L / nx
from fipy.meshes.grid1D import Grid1D
mesh = Grid1D(dx = dx, nx = nx)
from fipy.variables.cellVariable import CellVariable
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