  Accurate numerical simulations of interaction between fluid and solid play an
important role in applications. The task is challenging in practical scenarios
as the media are usually highly heterogeneous with very large contrast. To
overcome this computational challenge, various multiscale methods are
developed. In this paper, we consider a class of linear poroelasticity problems
in high contrast heterogeneous porous media, and develop a mixed generalized
multiscale finite element method (GMsFEM) to obtain a fast computational
method. Our aim is to develop a multiscale method that is robust with respect
to the heterogeneities and contrast of the media, and gives a mass conservative
fluid velocity field. We will construct decoupled multiscale basis functions
for the elastic displacement as well as fluid velocity. Our multiscale basis
functions are local. The construction is based on some suitable choices of
local snapshot spaces and local spectral decomposition, with the goal of
extracting dominant modes of the solutions. For the pressure, we will use
piecewise constant approximation. We will present several numerical examples to
illustrate the performance of our method. Our results indicate that the
proposed method is able to give accurate numerical solutions with a small
degree of freedoms.
