Enriched multi-point flux approximation for general grids

  • Authors:

  • Qian-Yong Chen;Jing Wan;Yahan Yang;Rick T. Mifflin

  • Affiliations:

  • Institute for Mathematics and its Applications, University of Minnesota, 207 Church Street S.E., Minneapolis, 55455-0134, United States;ExxonMobil Upstream Research Company, Houston, TX, United States;ExxonMobil Upstream Research Company, Houston, TX, United States;ExxonMobil Upstream Research Company, Houston, TX, United States

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2008

Quantified Score

Hi-index 31.46

Visualization

Abstract

It is well known that the two-point flux approximation, a numerical scheme used in most commercial reservoir simulators, has O(1) error when grids are not K-orthogonal. In the last decade, the multi-point flux approximations have been developed as a remedy. However, non-physical oscillations can appear when the anisotropy is really strong. We found out the oscillations are closely related to the poor approximation of pressure gradient in the flux computation. In this paper, we propose the control volume enriched multi-point flux approximation (EMPFA) for general diffusion problems on polygonal and polyhedral meshes. Non-physical oscillations are not observed for realistic and strongly anisotropic heterogeneous material properties described by a full tensor. Exact linear solutions are recovered for grids with non-planar interfaces, and a first and second order convergence are achieved for the flux and scalar unknowns, respectively.