An adaptive multiscale method for simulation of fluid flow in heterogeneous porous media

Several multiscale methods for elliptic problems that provide high resolution velocity fields at low computational cost have been applied to porous media flow problems. However, to achieve enhanced accuracy in the flow simulation, the numerical scheme for modeling the transport must account for the fine scale structures in the velocity field. To solve the transport equation on the fine scale with conventional finite volume methods will often be prohibitively computationally expensive for routine simulations. In this paper we propose a more efficient adaptive multiscale method for solving the transport equation. In this method the global flow is computed on a coarse grid scale, while at the same time honoring the fine scale information in the velocity field. The method is tested on both two- and three-dimensional test cases with complex heterogeneous structures. The numerical results demonstrate that the adaptive multiscale method gives nearly the same flow characteristics as simulations where the transport equation is solved on the scale of an underlying fine grid. Some analysis is presented to estimate error sources and support our conclusions from the numerical results.