Good morning!
Recently, I start to use fipy to solve partial differential equations, but
was stuck in the boundary conditions constrain. I want to constrain the
variable P(x,t) within the system, but can't stop it from flowing out of
the system. I tried all kinds of boundary condition in fipy, but all
failed.
Below is the two coupled equations, with the code that I write, please
correct me if I am wrong, I would be very grateful, since I don't have any
friends who has used fipy to discuss with. Therefore, any of your
suggestions would be much appreciated.
Best regards
Jiang
Graduate students of UW
Equations:
∇2*V*(x,t)=-a1* *P*(x, t)
d*P*(x, t)/dt = a2* ∇(∇*V*(x,t)**P*(x,t))
boundary condition :
y01=np.zero(nx)
y01[30 :70]=1e21
P(x, t=0) = y01
L=1e-6, nx=100, dx= L/nx, a1= 7.23164*e10, a2=1.1e-13
*import *numpy *as *np
*import *matplotlib.pyplot *as *plt
*from *fipy *import *Variable, FaceVariable, CellVariable, Grid1D,
TransientTerm, DiffusionTerm, Viewer, ConvectionTerm
L=1e-6
nx=100
dx= L/nx
a1=7.23164e-10
a2=1.1e-13
x = np.linspace(0, L, nx)
y01 = np.zeros(nx)
y01[30:70] = 1e21
mesh = Grid1D(dx=dx, nx=nx)
P_variable = CellVariable(mesh=mesh, name=*'Positive Charge Density'*, value=
y01)
V_variable = CellVariable (mesh=mesh, name=*'potential'*, value=0.)
Eqn1 = DiffusionTerm(coeff=1, var=V_variable) == -a1 * P_variable
Eqn2 = TransientTerm(coeff=1, var=P_variable) == a2 *
DiffusionTerm(coeff=P_variable,
var=V_variable)
V_variable.constrain(0., mesh.exteriorFaces)
*# P_variable.faceGrad.constrain(0., mesh.exteriorFaces) *eq = Eqn1 & Eqn2
steps = 1000
time_step = 0.1
*for *step *in *range(steps):
eq.solve(dt=time_step)
*if *step%1000==0:
viewer = Viewer(vars=(P_variable,), datamin=0, datamax=1.5e21)
*# plt.pause(1)*
viewer.plot()
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