A Multipoint Flux Approximation Method Using Different Interpolation Startegies for Oil Resevoir Simulation

Abstract

In the present work, we seek to present a robust and accurate finite volume based on scheme discretization of the pressure equation for oil reservoirs in highly heterogeneous and anisotropic media, adopting distorted polygonal meshes. This discretization methodology is based on a multipoint flux approximation with a quasi-local stencil method (MPFA-QL). This type of approach occurs through a co-normal decomposition that determines the physical direction of the flux on the control surface. Thus, we build the one-sided flux for each control surface and then obtain a unique flux expression through a convex combination of these. Then, the auxiliary variables located at the vertex that define the control surfaces are interpolated using different interpolation strategies. Our goal is to analyze and categorize how the robustness and accuracy of the numerical solution to the pressure equation are influenced by the different adopted interpolation strategies.