Hi all,
I have a highly nonlinear diffusion problem whose diffusion
coefficient can vary as T^alpha where alpha can range from 1 to 4.
Such problems occur in radiative transfer (alpha=3.5) often. I
modified the example 10 and took parts of the navier-stokes example to
create a new one to solve this problem. The boundary conditions are of
the mixed type (Robin) and hence acts as the source for the energy
wave that propagates in to the domain as time proceeds.
The issue is that I get negative temperatures at the first element
during assembly, immaterial of the refinement or the resolution of the
domain. I do not understand this behavior and was wondering if there
was a requirement with continuous FEM (Lagrange basis) that was not
satisfied in these problems with non-smooth solutions. I am certain
that there should be a fix to make sure that negative solutions are
avoided and that energy was conserved. But all my literature search
has not led to any decent solutions yet.
I've attached the example and the makefile for the libmesh program
which demonstrates this issue. Any suggestions for obtaining valid
solutions will be much appreciated.
The command line for my run looks like
./nonlinear-opt -init_timestep 0 -n_timesteps 2000 -dt 0.0005 -n 100
-n_refinements 0
Also, if you find any bugs in the implementation, please do let me
know. Also, since it is a time-dependent, nonlinear problem, when
resolved, it could make as a good example program. Just a thought !
Thanks,
Vijay
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