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

Aron Roland aaronroland at gmx.de
Mon Feb 24 16:30:29 CST 2014


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 ...



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 
> <mailto:jed at jedbrown.org>> wrote:
>     Christophe Ortiz <christophe.ortiz at ciemat.es
>     <mailto: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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