  In this paper, we consider the numerical solution of poroelasticity problems
that are of Biot type and develop a general algorithm for solving coupled
systems. We discuss the challenges associated with mechanics and flow problems
in heterogeneous media. The two primary issues being the multiscale nature of
the media and the solutions of the fluid and mechanics variables traditionally
developed with separate grids and methods. For the numerical solution we
develop and implement a Generalized Multiscale Finite Element Method (GMsFEM)
that solves problem on a coarse grid by constructing local multiscale basis
functions. The procedure begins with construction of multiscale bases for both
displacement and pressure in each coarse block. Using a snapshot space and
local spectral problems, we construct a basis of reduced dimension. Finally,
after multiplying by a multiscale partitions of unity, the multiscale basis is
constructed in the offline phase and the coarse grid problem then can be solved
for arbitrary forcing and boundary conditions. We implement this algorithm on
two heterogenous media and compute error between the multiscale solution with
the fine-scale solutions. Randomized oversampling and forcing strategies are
also tested.
