## 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.