hi,
i scanned the list and the documentation but have not been able to make
this work properly yet:
i have a 2D pde of the form
\[
\partial_t \rho = \nabla \cdot (\rho \nabla \phi) + D \nabla^2 \rho +
\lambda \rho
\]
where phi is a potential field and lambda is a source field, both are
constant in time and smoothly varying in space.
i have been solving this with fipy, using
DiffusionTermCorrection(coeff=[D,]) for the diffusion
PowerLawConvectionTerm(coeff=v ) where v = -phi.grad for the advection
ImplicitSourceTerm(coeff=lambda) for the source
the boundary conditions are either no-flux or dirichlet. i think
advection is dominant, although i can't say i have actually tried to
quantify that.
i am testing the solution by subtracting the rhs and lhs of the equation
and comparing that to \partial_t \rho in magnitude. i am having trouble
making this error smaller than around 10%: at points where the density
grows strongly, the solution deviates.
at the moment i am using a loop like this:
for (st, stnext) in zip(Solve.sample_t, Solve.sample_t[1:]):
for tt in nx.arange(st, stnext, Solve.step):
rho.updateOld()
res = 1.
while res > Solve.tolerance:
res = eq.sweep(var=rho, dt=Solve.step)
i've played around with making the mesh smaller -- did not seem to make
any difference; reducing the tolerance -- some effect, and reducing the
temporal step size, which did not help much.
should i be doing something differently?
thanks for any help!
n.
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