IMA Postdoc Seminar (March 30, 2010)

Speaker:Jiang, Lijian (IMA)

Title:Multiscale simulations for flows in heterogeneous porous media.

Abstract: Processes in heterogeneous porous media are affected by many scales ranging from pore scale to the field scales. For many simulations, it is prohibitively expensive to perform computations at the finest scales. Some type of coarsening is needed, especially for solving complex processes and large-scale inverse problems. Due to complex heterogeneities at the finest scales, simple coarse partitionings of the spatial as well as temporal regions are not possible. For example, in fractured materials, it is impossible to encompass highly conducting fracture regions into a coarse block. For this reason, subgrid models are needed to accurately represent small-scale information on a coarse grid. In this talk, I will discuss various subgrid models within the framework of mixed multiscale finite element methods. The main idea of mixed multiscale finite element methods is to incorporate small-scale information into multiscale basis functions that are used to solve flow equations on a coa rse grid. I will discuss how one can construct these basis functions so that the small-scale information is accurately captured on a coarse grid. The extnesions to stochastic flow equations and wave equations will be also mentioned. Numerical results using complex heterogeneities will be presented.