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 :-( !
