def GetAz(Bx, By, Jz, Nc, dl):
mesh = Grid2D(dx=dl[0], dy=dl[1], nx=Nc[0], ny=Nc[1])
_Az = CellVariable(mesh=mesh, value=0.0)
_Bx = CellVariable(mesh=mesh)
_Bx.value = np.reshape(Bx, Nc[0] * Nc[1], order='F')
_By = CellVariable(mesh=mesh)
_By.value = np.reshape(By, Nc[0] * Nc[1], order='F')
_Jz = CellVariable(mesh=mesh)
_Jz.value = np.reshape(Jz, Nc[0] * Nc[1], order='F')
_Az.equation = (DiffusionTerm(coeff=1.0) + _Jz == 0)
# beware of the sign of the flux : always consider outward direction
BCs = [
FixedFlux(value=_By.getFaceValue(), faces=mesh.getFacesLeft()),
FixedFlux(value=-_By.getFaceValue(), faces=mesh.getFacesRight()),
FixedFlux(value=-_Bx.getFaceValue(), faces=mesh.getFacesBottom()),
FixedFlux(value=_Bx.getFaceValue(), faces=mesh.getFacesTop())
]
_Az.equation.solve(var=_Az, boundaryConditions=BCs)
Az = np.reshape(_Az.value, Nc, order='F')
return Az
def GetAz(Bx, By, Jz, Nc, dl):
mesh = Grid2D(dx=dl[0], dy=dl[1], nx=Nc[0], ny=Nc[1])
_Az = CellVariable(mesh=mesh, value=0.0)
_Bx = CellVariable(mesh=mesh)
_Bx.value = np.reshape(Bx, Nc[0] * Nc[1], order='F')
_By = CellVariable(mesh=mesh)
_By.value = np.reshape(By, Nc[0] * Nc[1], order='F')
_Jz = CellVariable(mesh=mesh)
_Jz.value = np.reshape(Jz, Nc[0] * Nc[1], order='F')
_Az.equation = (DiffusionTerm(coeff=1.0) + _Jz == 0)
#diffcoeff = CellVariable(mesh=mesh, value = 1.0)
#diffTerm = DiffusionTerm(coeff = diffcoeff)
#diffTerm = DiffusionTerm(coeff = 1.0)
#diffcoeff.constrain(0., mesh.exteriorFaces)
# beware of the sign of the flux : always consider outward direction
_Az.faceGrad.constrain(_By.arithmeticFaceValue, where=mesh.facesLeft)
_Az.faceGrad.constrain(-_By.arithmeticFaceValue, where=mesh.facesRight)
_Az.faceGrad.constrain(-_Bx.arithmeticFaceValue, where=mesh.facesBottom)
_Az.faceGrad.constrain(_Bx.arithmeticFaceValue, where=mesh.facesTop)
#_Az.faceGrad.constrain( _By.arithmeticFaceValue[mesh.facesLeft] , where=mesh.facesLeft)
#_Az.faceGrad.constrain(-_By.arithmeticFaceValue[mesh.facesRight] , where=mesh.facesRight)
#_Az.faceGrad.constrain(-_Bx.arithmeticFaceValue[mesh.facesBottom] , where=mesh.facesBottom)
#_Az.faceGrad.constrain( _Bx.arithmeticFaceValue[mesh.facesTop] , where=mesh.facesTop)
#_Az.equation = (diffTerm+_Jz == 0)
#_Az.equation = (DiffusionTerm(diffcoeff)+ (mesh.exteriorFaces*exteriorFlux).divergence + _Jz== 0)
#_Az.equation = (diffTerm + _Jz == 0)
#BCs = [FixedFlux(value= _By.getFaceValue(), faces=mesh.getFacesLeft()),
# FixedFlux(value=-_By.getFaceValue(), faces=mesh.getFacesRight()),
# FixedFlux(value=-_Bx.getFaceValue(), faces=mesh.getFacesBottom()),
# FixedFlux(value= _Bx.getFaceValue(), faces=mesh.getFacesTop())]
#_Az.equation.solve(var=_Az, boundaryConditions=BCs)
_Az.equation.solve(var=_Az)
Az = np.reshape(_Az.value, Nc, order='F')
return Az
return a1 * np.sin(b1 * x + c1) + a2 * np.sin(b2 * x + c2)
mesh = Grid1D(dx=dx, nx=nx)
Pion = CellVariable(mesh=mesh,
name='Positive ion Charge Density',
value=y01(mesh.x))
Nion = CellVariable(mesh=mesh,
name='Negative ion Charge Density',
value=y02(mesh.x))
potential = CellVariable(mesh=mesh, name='Potential', value=y03(mesh.x))
Jp = CellVariable(mesh=mesh, name='Positive ion Current Density', value=0.)
Jn = CellVariable(mesh=mesh, name='Negative ion Current Density', value=0.)
Jp.value = -mu_p * Pion * potential.arithmeticFaceValue.divergence + Dn * Pion.arithmeticFaceValue.divergence
Jn.value = -mu_n * Nion * potential.arithmeticFaceValue.divergence + Dn * Pion.arithmeticFaceValue.divergence
Pion.equation = TransientTerm(
coeff=1,
var=Pion) == -k_rec * Pion * Nion + (Jp.arithmeticFaceValue).divergence
Nion.equation = TransientTerm(
coeff=1,
var=Nion) == -k_rec * Pion * Nion - (Jn.arithmeticFaceValue).divergence
potential.equation = DiffusionTerm(coeff=epsilon, var=potential) == Pion - Nion
Pion.constrain(0., where=mesh.facesLeft)
Pion.constrain(0., where=mesh.facesRight)
Nion.constrain(0., where=mesh.facesLeft)
Nion.constrain(0., where=mesh.facesRight)
potential.constrain(0., where=mesh.facesLeft)
import glob as glob import re import os # Setting up a mesh nx = 50 dx = 0.02 L = nx * dx mesh = Grid1D(nx=nx, dx=dx) # Defining the cell variable c = CellVariable(mesh=mesh, name=r"$c$") # Initialise c with a funky profile x = mesh.cellCenters[0] c.value = 0.0 c.setValue((0.3 * numerix.sin(2.0 * x * numerix.pi)) + 0.5) # Setting up the no-flux boundary conditions c.faceGrad.constrain(0.0, where=mesh.facesLeft) c.faceGrad.constrain(0.0, where=mesh.facesRight) # Provide value for diffusion and reaction coefficient D = 1.0 k = -2.0 # Specifying our alpha value. We will only use backwards Euler going forward alpha = 1 # Defining the equation with the reaction term. eq = TransientTerm() == DiffusionTerm(coeff=D) + ImplicitSourceTerm(coeff=k)
from fipy import CellVariable, GaussianNoiseVariable, DiffusionTerm, TransientTerm, ImplicitSourceTerm, VTKCellViewer, LinearLUSolver, PeriodicGrid1D, Viewer, UniformNoiseVariable, Grid1D from fipy.tools import numerix from math import log nx = 100 dx = 0.3 mesh = Grid1D(dx=dx, nx=nx) phi = CellVariable(name=r"$\phi$", mesh=mesh) psi = CellVariable(name=r"$\psi$", mesh=mesh) # noise = GaussianNoiseVariable(mesh=mesh, mean=0.8, variance=0.002).value # phi[:] = noise x = mesh.cellCenters[0] phi.value = 0.1 phi.setValue(0.2, where=x < 0.3*(nx*dx)) phi.setValue(0.6, where=x > 0.3*(nx*dx)) phi.setValue(0.2, where=x > 0.32*(nx*dx)) phi.setValue(0.6, where=x > 0.7*(nx*dx)) phi.setValue(0.2, where=x > 0.72*(nx*dx)) D = a = epsilon = 1. N_A = 500 N_B = 500 chi_AB = 0.015 kappa = 2*chi_AB / 3.0 dfdphi = ((1.0/N_A) - (1.0/N_B)) + (1.0/N_A)*numerix.log(phi) - (1.0/N_B)*numerix.log(1.0 - phi) + chi_AB*(1.0 - 2*phi)
