Thank you so much. I just realized the solution this morning, which
agrees with your answer. It is a stupid question. But I got stuck for
days because I had one-track mind that the nabla terms must be fully
expanded in following way: \nabla^2 \phi^2 = 2 (\nabla \phi) \cdot
(\nabla \phi) + 2 \phi (\nabla^2 \phi)
Then I stuck at implementing (\nabla \phi) \cdot (\nabla \phi) which is
not applicable in Fipy.
Thanks again.
On 26/01/15 20:25, Guyer, Jonathan E. Dr. wrote:
An _OperatorVariable is an internal FiPy object that represents a mathematical
operation, such as phi**2. By saying 'var=phi**2' you are telling FiPy to solve
for phi**2 rather than for phi. The error is telling you that FiPy doesn't know
how to do that.
DiffusionTerm(var=???, coeff=D) represents \nabla\cdot D \nabla ???, where ???
must be a solution variable, not a function of a solution variable. FiPy builds
systems of linear equations (like any other finite-(difference|volume|element)
code), so each of the terms must be a linear expression of a solution variable.
The thing to do here is carry the derivatives through to put these expressions
in a form FiPy understands:
d\phi/d t = \nabla^2 \phi + \nabla^2 \phi^2 + \nabla^2 \phi^3
= \nabla \cdot \nabla \phi + \nabla\cdot(2\phi \nabla \phi) +
\nabla\cdot(3\phi^2 \nabla \phi)
There's no reason not to condense this to
d\phi/d t = \nabla \cdot[(1 + 2\phi + 3\phi^2)\nabla \phi]
or
PHI = phi.faceValue
TransientTerm(coeff=1., var=phi) == DiffusionTerm(coeff=1 + 2*PHI + 3*PHI**2,
var=phi)
On Jan 26, 2015, at 12:09 PM, Ronghai Wu <ronghai...@fau.de> wrote:
Dear Fipy developers and users,
I have a strange PDE in 2D "dphi/dt = Laplacian(phi) + Laplacian(phi**2) +
Laplacian(phi**3)",
which I implement in the following way, but raise typeerror "The value of an
`_OperatorVariable` cannot be assigned". Can anyone help me? Thanks.
dx = 0.1
dy = dx
nx = 100
ny = nx
mesh = Grid2D(dx=dx, dy=dy, nx=nx, ny=ny)
x = mesh.cellCenters[0]
y = mesh.cellCenters[1]
phi =
CellVariable(mesh=mesh, hasOld=1, value=x*y)
eq = TransientTerm(var=phi, coeff=1.) ==
ImplicitDiffusionTerm(var=phi, coeff=1.) +
ImplicitDiffusionTerm(var=phi**2, coeff=1.) +
ImplicitDiffusionTerm(var=phi**3, coeff=1.)
viewer = Viewer(vars=phi)
for step in range(10):
phi.updateOld()
res = 1.e5
while res > 1.e-1:
res = eq.sweep(dt=1.e-3)
viewer.plot()
Regards
Ronghai
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--
------------------------------------------
Ronghai Wu
Institute of Materials Simulation (WW8)
Department of Materials Science and Engineering
University of Erlangen-Nürnberg
Dr.-Mack-Str. 77, 90762 Fürth, Germany
Tel. +49 (0)911 65078-65064
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