Hi,
I can provide u some nice package to generate unstructured meshes. There
are many institutions using it now. We have also used PETSC to solve
some nonlinera hyperbolic problem on 2d on unstructured meshes and it
works quite ok even if the scaling still not what it should be but well
these are other issues ...
Cheers
Aron
On 02/24/2014 09:04 AM, Christophe Ortiz wrote:
On Sat, Feb 22, 2014 at 2:33 AM, Jed Brown <[email protected]
<mailto:[email protected]>> wrote:
Christophe Ortiz <[email protected]
<mailto:[email protected]>> writes:
> Hi all,
>
> Recently I have implemented a 1D problem of coupled diffusion
equations
> using PETSc. I did it using finite differences for diffusion
terms and
> F(t,U,U_t) = 0. It works pretty well with ARKIMEX3. I get a nice
timestep
> variation and all boundary conditions work well.
>
> Now I would like to move to 3D problems to simulate the
diffusion and
> interaction of species in a "real material". By real material I
mean a
> material made of subregions with internal surfaces where species
could
> recombine (means Dirichlet). These subregions are distributed in a
> complicated manner, ie not cartesian. A good picture of this
would be a
> polycrystal (see attachment to get an idea). Each crystal has a
different
> orientation and the boundary between two small crystals forms an
internal
> surface.
>
> I have several questions on how to implement this:
>
> 1) Since, the problem will not be solved in a cartesian mesh,
should I use
> unstructured meshes ? If so, how can this unstructured mesh can be
> generated ( I have no experience with unstructured meshes. I
always work in
> 1D).
Are you intending to mesh the boundaries of the crystals? Will you be
dynamically remeshing? (That is very complicated and expensive in
3D.)
What formulation will you be using for grain boundary evolution?
No, in principle I will not consider the evolution of grains.
Therefore, no dynamic remershing (in principle).
What I want is just the evolution of diffusing and reacting species
inside the ensemble of grains, including their interaction with the
grain boundaries (trapping, segregation, ...).
I think you should check out phase field models, such as the
publication
below.
I never used phase-field models. According to what I read, it can
model many phnomena but in particular it substitutes a boundary
condition at an interface by a PDE for the evolution of an auxiliary
field (Wikipedia). In this sense, maybe it could be interesting since
I want to simulate the evolution of species inside grains with many
internal grain boundaries.
But I don't know if to treat a grain boundary as a infinitely sharp
interface or as a thin but finite piece of material with different
properties for species (diffusion coeff for instance).
Perhaps check out the paper below. The framework (MOOSE) used
for this publication should be released open source on github next
week
(check https://github.com/idaholab/). I don't know if Marmot, the
phase-field component, will be open source any time soon, but they are
typically happy to collaborate. MOOSE uses PETSc for solvers, but
provides a higher level interface.
@article{tonks2012object,
title={An object-oriented finite element framework for
multiphysics phase field simulations},
author={Tonks, M.R. and Gaston, D. and Millett, P.C. and Andrs,
D. and Talbot, P.},
journal={Computational Materials Science},
volume={51},
number={1},
pages={20--29},
year={2012},
publisher={Elsevier}
}
Sorry, I could not download the article. We don't have access. Crisis
in Spain :-( !
