Hi, On Mon, Feb 24, 2014 at 11:30 PM, Aron Roland <[email protected]> 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 <[email protected]> wrote: > >> Christophe Ortiz <[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 :-( ! > > > >
