Hi ray,
Casting the implicit PDE does not work for my problem. FiPy throws up a ton of
errors.
I am attaching a minimal example (based off example1.mesh.1D)
from fipy import *
nx = 50
dx = 1.
mesh = Grid1D(nx=nx, dx=dx)
phi = CellVariable(name="field variable", mesh=mesh, value=0.0)
D = 1.
valueLeft = 0.0
phi.constrain(valueLeft, mesh.facesLeft)
phi.faceGrad.constrain([phi], mesh.facesRight) # This is the problematic BC
eq = TransientTerm() == DiffusionTerm(coeff=D)
timeStep = 0.9 * dx**2 / (2 * D)
steps = 100
viewer = Viewer(vars=phi)
for step in range(steps):
eq.solve(var=phi, dt=timeStep)
viewer.plot()
The errors are as follows:
line 22, in <module>
eq.solve(var=phi, dt=timeStep)
\fipy\terms\term.py", line 211, in solve
solver = self._prepareLinearSystem(var, solver, boundaryConditions, dt)
\fipy\terms\term.py", line 170, in _prepareLinearSystem
buildExplicitIfOther=self._buildExplcitIfOther)
\fipy\terms\binaryTerm.py", line 68, in _buildAndAddMatrices
buildExplicitIfOther=buildExplicitIfOther)
\fipy\terms\unaryTerm.py", line 99, in _buildAndAddMatrices
diffusionGeomCoeff=diffusionGeomCoeff)
\fipy\terms\abstractDiffusionTerm.py", line 337, in _buildMatrix
nthCoeffFaceGrad = coeff[numerix.newaxis] * var.faceGrad[:,numerix.newaxis]
\fipy\variables\variable.py", line 1575, in __getitem__
unit=self.unit,
\fipy\variables\variable.py", line 255, in _getUnit
return self._extractUnit(self.value)
\fipy\variables\variable.py", line 561, in _getValue
value[..., mask] = numerix.array(constraint.value)[..., mask]
IndexError: index 50 is out of bounds for axis 1 with size 50
I have tried including the implicit BC within the time-stepper loop, but that
does not still help.
Best Regards
Krishna
From: [email protected] [mailto:[email protected]] On Behalf Of
Gopalakrishnan, Krishnakumar
Sent: 08 June 2016 23:42
To: [email protected]
Subject: RE: casting implicit Boundary Conditions in FiPy
Hi Raymond,
Sorry, it was a typo.
Yes, It is indeed d (phi)/dx, the spatial derivative BC. I shall try setting
phi.faceGrad.constrain([k*phi], mesh.facesRight), and see if it will work.
Thanks for pointing this out.
Krishna
From: [email protected]<mailto:[email protected]>
[mailto:[email protected]] On Behalf Of Raymond Smith
Sent: 08 June 2016 23:36
To: [email protected]<mailto:[email protected]>
Subject: Re: casting implicit Boundary Conditions in FiPy
Hi, Krishna.
Just to make sure, do you mean that the boundary condition is a derivative with
respect to the spatial variable or with respect to time as-written? If you mean
spatial, such that d\phi/dx = k*phi, have you tried
phi.faceGrad.constrain(k*phi) and that didn't work?
If you mean that its value is prescribed by its rate of change, then I'm not
sure the best way to do it. Could you maybe do it explicitly?
- Store the values from the last time step with hasOld set to True in the
creation of the cell variable
- In each time step, calculate the backward-Euler time derivative manually and
then set the value of phi with the phi.constrain method.
Ray
On Wed, Jun 8, 2016 at 6:26 PM, Gopalakrishnan, Krishnakumar
<[email protected]<mailto:[email protected]>>
wrote:
I am trying to solve the standard fickean diffusion equation on a 1D uniform
mesh in (0,1)
$$\frac{\partial \phi}{\partial t} = \nabla.(D \nabla\phi)$$
with a suitable initial value for $\phi(x,t)$.
The problem is that, one of my boundary conditions is implicit, i.e. is a
function of the field variable being solved for.
$ \frac{\partial\phi}{\partial t} = k \phi $ , at the right boundary edge, k =
constant
The left BC is not a problem, it is just a standard no-flux BC.
How do I cast this implicit BC in FiPy ? Any help/pointers will be much
appreciated.
Best regards
Krishna
Imperial College London
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