A nonlinear repair technique for the MPFA-D scheme in single-phase flow problems and heterogeneous and anisotropic media
A. Castiel Reis de Souza (TU Delft - Numerical Analysis)
Diego D B Carvalho ( Universidade Federal de Pernambuco)
Túlio de Moura Cavalcante ( Universidade Federal de Pernambuco)
Fernando Raul Licapa Contreras ( Universidade Federal de Pernambuco)
Michael G. Edwards (Swansea University)
Paulo Roberto Maciel Lyra ( Universidade Federal de Pernambuco)
More Info
expand_more
Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.
Abstract
A novel Flux Limited Splitting (FLS) non-linear Finite Volume (FV) method for families of linear Control Volume Distributed Multi Point Flux Approximation (CVD-MPFA) schemes is presented. The new formulation imposes a local discrete maximum principal (LDMP) which ensures that the discrete solution is free of spurious oscillations. The FLS scheme can be seen as a natural extension of the M-Matrix Flux Splitting method that splits the MPFA flux components in terms of the Two-Point Flux Approximation (TPFA) flux and Cross Diffusion Terms (CDT), with the addition of a dynamically computed relaxation parameter to the CDT that identifies and locally corrects the regions where the LDMP is violated. Moreover, the whole non-linear procedure was devised as a series of simple straightforward matrix operations. The methodology is presented considering the Multi-Point Flux Approximation with a Diamond (MPFA-D) in what we call the FLS + MPFA-D formulation which is tested using a series of challenging benchmark problems. For all test cases, the FLS repair technique imposes the LDMP and eliminates the spurious oscillations induced by the original MPFA-D method.
help_outline