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Accurate numerical simulations of interaction between fluid and solid play animportant role in applications. The task is challenging in practical scenariosas the media are usually highly heterogeneous with very large contrast. Toovercome this computational challenge, various multiscale methods aredeveloped. In this paper, we consider a class of linear poroelasticity problemsin high contrast heterogeneous porous media, and develop a mixed generalizedmultiscale finite element method (GMsFEM) to obtain a fast computationalmethod. Our aim is to develop a multiscale method that is robust with respectto the heterogeneities and contrast of the media, and gives a mass conservativefluid velocity field. We will construct decoupled multiscale basis functionsfor the elastic displacement as well as fluid velocity. Our multiscale basisfunctions are local. The construction is based on some suitable choices oflocal snapshot spaces and local spectral decomposition, with the goal ofextracting dominant modes of the solutions. For the pressure, we will usepiecewise constant approximation. We will present several numerical examples toillustrate the performance of our method. Our results indicate that theproposed method is able to give accurate numerical solutions with a smalldegree of freedoms.

Mixed GMsFEM for linear poroelasticity problems in heterogeneous porous media