temperature = CellVariable(
name='temperature',
mesh=mesh,
value=initialTemperature,
hasOld=1
)
bench.stop('variables')
bench.start()
from fipy.tools import numerix
mVar = phase - 0.5 - kappa1 / numerix.pi * \
numerix.arctan(kappa2 * temperature)
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)) + \
sweeps=10
from fipy.meshes.grid2D import Grid2D
mesh = Grid2D(nx=N, ny=N, dx=dL, dy=dL)
from fipy.variables.cellVariable import CellVariable
psi = CellVariable(mesh=mesh, name='stream function')
Xhat=(1,0)
Yhat=(0,1)
u=psi.getGrad().dot(Yhat)
v=-psi.getGrad().dot(Xhat)
U=psi.getFaceGrad()
from fipy.terms.implicitDiffusionTerm import ImplicitDiffusionTerm
eq=ImplicitDiffusionTerm(0.00001) \
+ u * u.getGrad().dot(Xhat) \
+ v * u.getGrad().dot(Yhat) \
- 2 * u.getGrad().dot(Yhat).getGrad().dot(Yhat)
from fipy.boundaryConditions.nthOrderBoundaryCondition import NthOrderBoundaryCondition
from fipy.boundaryConditions.fixedValue import FixedValue
BC = (NthOrderBoundaryCondition(faces=mesh.getFacesBottom(), value=0,order=1),
FixedValue(faces=mesh.getFacesBottom(), value=0),
NthOrderBoundaryCondition(faces=mesh.getFacesLeft(), value=0,order=1),
NthOrderBoundaryCondition(faces=mesh.getFacesTop(), value=1,order=1),
where=(x - seedCenter[0])**2 +
(y - seedCenter[1])**2 < radius**2)
temperature = CellVariable(name='temperature',
mesh=mesh,
value=initialTemperature,
hasOld=1)
bench.stop('variables')
bench.start()
from fipy.tools import numerix
mVar = phase - 0.5 - kappa1 / numerix.pi * \
numerix.arctan(kappa2 * temperature)
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)) + \
sweeps=10 from fipy.meshes.grid2D import Grid2D mesh = Grid2D(nx=N, ny=N, dx=dL, dy=dL) from fipy.variables.cellVariable import CellVariable u = CellVariable(mesh=mesh, name='X velocity') v = CellVariable(mesh=mesh, name='Y velocity') from fipy.variables.vectorFaceVariable import VectorFaceVariable velocity = VectorFaceVariable(mesh=mesh) Xhat=(1,0) Yhat=(0,1) velocity=u.getFaceGrad().dot(Xhat) * Xhat + v.getFaceGrad().dot(Yhat) * Yhat from fipy.terms.implicitDiffusionTerm import ImplicitDiffusionTerm diffTerm=ImplicitDiffusionTerm(coeff=viscosity) from fipy.terms.exponentialConvectionTerm import ExponentialConvectionTerm convTerm = ExponentialConvectionTerm(coeff = velocity,diffusionTerm = diffTerm) eq1= diffTerm - u * u.getGrad().dot(Xhat) - v * u.getGrad().dot(Yhat) eq2= velocity.getDivergence() #eq2= u.getGrad() + v.getGrad() eq2=u.getFaceGrad().dot(Xhat) * Xhat + v.getFaceGrad().dot(Yhat) * Yhat eq2= u.getGrad().dot(Xhat) + v.getGrad().dot(Yhat) eq2= ImplicitDiffusionTerm(1) + u.getGrad().dot(Xhat) + v.getGrad().dot(Yhat)
sweeps = 10 from fipy.meshes.grid2D import Grid2D mesh = Grid2D(nx=N, ny=N, dx=dL, dy=dL) from fipy.variables.cellVariable import CellVariable u = CellVariable(mesh=mesh, name='X velocity') v = CellVariable(mesh=mesh, name='Y velocity') from fipy.variables.vectorFaceVariable import VectorFaceVariable velocity = VectorFaceVariable(mesh=mesh) Xhat = (1, 0) Yhat = (0, 1) velocity = u.getFaceGrad().dot(Xhat) * Xhat + v.getFaceGrad().dot(Yhat) * Yhat from fipy.terms.implicitDiffusionTerm import ImplicitDiffusionTerm diffTerm = ImplicitDiffusionTerm(coeff=viscosity) from fipy.terms.exponentialConvectionTerm import ExponentialConvectionTerm convTerm = ExponentialConvectionTerm(coeff=velocity, diffusionTerm=diffTerm) eq1 = diffTerm - u * u.getGrad().dot(Xhat) - v * u.getGrad().dot(Yhat) eq2 = velocity.getDivergence() #eq2= u.getGrad() + v.getGrad() eq2 = u.getFaceGrad().dot(Xhat) * Xhat + v.getFaceGrad().dot(Yhat) * Yhat eq2 = u.getGrad().dot(Xhat) + v.getGrad().dot(Yhat) eq2 = ImplicitDiffusionTerm(1) + u.getGrad().dot(Xhat) + v.getGrad().dot(Yhat)
