Print Email Facebook Twitter A nonlinear repair technique for the MPFA-D scheme in single-phase flow problems and heterogeneous and anisotropic media Title A nonlinear repair technique for the MPFA-D scheme in single-phase flow problems and heterogeneous and anisotropic media Author Castiel Reis de Souza, A. (TU Delft Numerical Analysis) Elisiário de Carvalho, Darlan Karlo (Universidade Federal de Pernambuco) de Moura Cavalcante, Túlio (Universidade Federal de Pernambuco) Licapa Contreras, Fernando Raul (Universidade Federal de Pernambuco) Edwards, Michael G. (Swansea University) Lyra, Paulo Roberto Maciel (Universidade Federal de Pernambuco) Date 2024 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. Subject Flux Limited Splitting (FLS)Non-linear Repair TechniqueDiscrete Maximum Principle (DMP)Heterogeneous and Anisotropic mediaUnstructured Meshes To reference this document use: http://resolver.tudelft.nl/uuid:575bc204-eebf-47ba-8bb8-15da7edd3f91 DOI https://doi.org/10.1016/j.jcp.2024.112759 ISSN 0021-9991 Source Journal of Computational Physics, 501 Part of collection Institutional Repository Document type journal article Rights © 2024 A. Castiel Reis de Souza, Darlan Karlo Elisiário de Carvalho, Túlio de Moura Cavalcante, Fernando Raul Licapa Contreras, Michael G. Edwards, Paulo Roberto Maciel Lyra Files PDF 1-s2.0-S0021999124000081-main.pdf 12.43 MB Close viewer /islandora/object/uuid:575bc204-eebf-47ba-8bb8-15da7edd3f91/datastream/OBJ/view