[petsc-users] From 1D to 3D problem ? Unstructured mesh ?

[Christophe Ortiz]

Hi,
On Mon, Feb 24, 2014 at 11:30 PM, Aron Roland <aaronroland at gmx.de> wrote:

>  Hi,
>
> I can provide u some nice package to generate unstructured meshes. There
> are many institutions using it now.
>

Yes, that would be great. Thanks !

Saludos,
Christophe


> 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 <jed at jedbrown.org> wrote:
>
>> Christophe Ortiz <christophe.ortiz at ciemat.es> 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 :-( !
>
>
>
>
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