Multiscale mixed/mimetic FEM on complex geometries
We consider a multiscale mixed finite element method (MsMFEM) for the modelling of porous media flow on models with complex geometrical features. The MsMFEM formulation is based on a hierarchical grid approach, where subscale effects are taken into account through the use of basis functions which are numerical solutions of local subscale/subgrid flow problems. By using these basis functions to discretize the global flow equations on a coarse grid, one can retain the efficiency of an upscaling method, while at the same time produce detailed and conservative velocity fields with subgrid resolution. In reservoir simulation, the subgrid is typically given by a geomodel represented in a corner-point grid format, which is the industry standard for modelling complex reservoir geometry. As a result, the subgrid may be highly irregular. Thus, to apply the MsMFEM to such models, there are mainly two challenges. First, one needs a stable and conservative subgrid-solver for the local flow problems, and second, one needs means of choosing suitable coarse grids.In this talk, we focus on the second challenge, coarse gridding for MsMFEM on models with complex geometrical features.One of the main advantages of the MsMFEM formulation is in the great flexibility with respect to grids. In fact, the coarse grid can in principle be any partition of the subgrid, where each coarse block is a connected collection of subgrid cells. However, we argue that in the process of generating coarse grids, one should follow certain simple guidelines to improve overall accuracy. Based on these guidelines, we discuss processing techniques aiming towards a fully automated gridding procedure. The presented methodology will be illustrated through numerical examples.
- SINTEF Digital / Mathematics and Cybernetics
6th International Congress on Industrial and Applied Mathematics (ICIAM 07). Minisymposium IC/MP/100/G/967, Complex flows: theoretical and computational aspects.
16.07.2007 - 20.07.2007