A generalized multiscale finite element method for high-contrast single-phase flow problems in anisotropic media

In this paper, we describe a systematic framework called the Generalized Multiscale Finite Element Method (GMsFEM) for performing multiscale simulations, and we investigate the application of this framework to the high-contrast flow problems in anisotropic media. We present a multiscale model reduction technique for constructing a reduced-dimension space based on localized spectral decompositions. We discuss the multiscale coarse space both in parameter-independent and parameter-dependent cases. Furthermore, we highlight the relation between the solution convergence and the spectral behavior of the eigenvalue problems. A variety of numerical examples are presented to illustrate the performance of the proposed methodology.