On Fri, Sep 7, 2018 at 12:16 PM Miguel Angel Salazar de Troya < [email protected]> wrote:
> Hi, > > I want to solve a simple Poisson equation with a diffusion coefficient, a > simple reaction term and apply Adaptive Mesh Ref (AMR). The problem is that > if the diffusion coefficient is much smaller than the mesh resolution (as > it can happen before applying AMR), I obtain over and undershoots of the > solution. I need this solution to be stable and not be over 1 or under 0 > (bounds from the source term). > > One way I was able to achieve this was by implementing a Finite Volume > solver within libMesh. Very easy for simple cartesian geometries. However, > now I need to extend it to non-cartesian geometries that are second order. > I am wondering if there are alternatives in libMesh to solve this > over/undershoot problem for the poisson equation. > If you have a reaction-dominated reaction/diffusion equation, you may be able to stabilize it using a Galerkin least-squares (GLS) formulation. There is a good discussion in the 1995 paper by Thompson: https://doi.org/10.1002/nme.1620380303 -- John _______________________________________________ Libmesh-users mailing list [email protected] https://lists.sourceforge.net/lists/listinfo/libmesh-users
