An iterative modified multiscale control volume method for the simulation of highly heterogeneous porous media flow

Abstract

In this paper, a modification of the multiscale finite-volume method (MsFVM) in its OBMM version (operator-based multiscale method) is introduced. The iterative modified multiscale control volume method (I-MMCVM) is applied to solve the elliptical problem that describes the single-phase fluid flow through heterogeneous porous media. The modifications proposed are accomplished by: (1) resettling the vertices, centroid of the primal coarse volume, of each primal coarse volume laying on the boundary of the computational domain, and by this, avoiding the use of ghost elements; (2) Recalculating the pressure iteratively in each primal coarse volume to improve the accuracy of the solution lost during the process of decoupling the problem in sub-problems. The I-MMCVM achieves efficiently accurate results for flow equations in highly heterogeneous reservoirs, at very low computational cost whilst it recovers physical consistency whenever the multiscale solution fails and produces nonphysical results. The I-MMCVM solution is compared with the fine mesh solution for some highly heterogeneous media. In terms of efficiency, the novel method showed great potential of the multiscale formulations, i.e., computational cost reduction without significant loss of accuracy.