Adaptive Variational Multiscale Methods for Multiphase Flow in Porous Media

Porous media are characterized by strongly heterogeneous properties on all scales of observation. This has motivated a sustained research effort in upscaling methods and lately multiscale methods. However, due to the lack of scale separation for realistic problems, static upscaling and multiscale methods may not be suitable in general, and adaptive approaches are needed. In this paper, we outline the application of an adaptive variational multiscale method for two-phase flow in porous media. We give the symmetric and nonsymmetric forms of the mixed variational multiscale method and suggest a framework for adaptively selecting the support of the fine scale Green's operators in space and time. The applicability of our framework is validated through a set of numerical comparisons.