A New Non-Orthodox Multipoint Flux Approximation Method (MPFA-HD) for the Simulation of One-Phase Problems in Anisotropic and Heterogeneous Porous Media

Fernando Raul Licapa Contreras¹; Paulo Roberto Maciel Lyra¹; Darlan Karlo Elisiario de Carvalho¹

¹ Universidade Federal de Pernambuco

doi:10.20906/CPS/CILAMCE2017-1127

Resumo

In the present paper, we present a new linear cell-centered finite volume Multipoint Flux Approximation Method (MPFA-HD) that uses a quasi-local stencil to approximate the steady-state one-phase flow problem in porous media using arbitrarily polygonal meshes that reproduces piecewise linear solutions exactly. The derivation of our linear MPFA-HD scheme is based on recently developed Non-Linear Finite Volume (NLFV) methods that are aimed to produce monotone solutions even for highly distorted meshes and strongly anisotropic media. In our linear scheme, we first construct the one-sided fluxes on each control surface independently and then a unique flux expression is obtained by a convex combination of the one sided fluxes. In order to improve the performance of our linear scheme for highly anisotropic permeability tensors, and differently from other classical MPFA methods, in our scheme, fluxes on each cell face are explicitly expressed by two cell centered unknowns belonging to two adjacent control volumes and points defined on vertices that do not necessarily belong to the same face shared by the adjacent cells, leading eventually to a non-local stencil. The unknown values at the required vertices are obtained by means of a linear preserving interpolation procedure, considering the surrounding control volumes to such vertices. To show the potential of our MPFA-HD finite volume formulation, we solve some benchmark problems found in literature. Our results are quite promising and generally superior to other classical MPFA methods (e.g., MPFA-O and MPFA-FPS) in term of accuracy and robustness, particularly for discontinuous and strongly anisotropic porous media.

Palavras-chave: One-phase Flow; Anisotropic and Heterogeneous Porous Media; MPFA-HD Finite Volume