A face-centred finite volume approach for coupled transport phenomena and fluid flow

Burcet，Martí1,2; Oliveira，Beñat2; Afonso，Juan Carlos2,3,5; Zlotnik，Sergio1,4

2024

10.1016/j.apm.2023.08.031

Applied Mathematical Modelling   Impact Factor & Quartile

0307-904X

1872-8480

We present a particular derivation of the face-centred finite volume (FCFV) method and study its performance in non-linear, coupled transport problems commonly encountered in geoscientific and geotechnical applications. The FCFV method is derived from the hybridisable discontinuous Galerkin formulation, using a constant degree of approximation for the discretization of the unknowns defined on the mesh faces (edges in two dimensions). The piecewise constant degrees of freedom are determined in a global problem over the mesh skeleton. Then, the solution and its gradient are recovered at the cells centroid in a set of element-by-element independent postprocesses, both exhibiting linear convergence. The formulation of the transient advection-diffusion-reaction equation is presented in detail and the numerical analysis under challenging advective/diffusive regimes is studied. Finally, we use several numerical examples to illustrate the advantages and limitations of the FCFV method to solve problems of geoscientific and geotechnical relevance governed by the non-linear coupling between advection-diffusion-reactive transport and Stokes flow. Our results show that the FCFV method is an attractive and highly competitive alternative to other commonly used methods.

Coupled problems Face-centred Finite volume methods Hybridisable discontinuous Galerkin

SCI

English

Corresponding

Generalitat de Catalunya[2017-SGR-1278];

Engineering ; Mathematics ; Mechanics

Engineering, Multidisciplinary ; Mathematics, Interdisciplinary Applications ; Mechanics

WOS:001077913600001

ELSEVIER SCIENCE INC

ENGINEERING

2-s2.0-85170438337

Scopus

1.Laboratori de Càlcul Numèric,LaCàN Universitat Politècnica de Catalunya,Barcelona,1, C/ Jordi Girona, Catalunya,08034,Spain
2.Earth and Environmental sciences,Macquarie University,Sydney,12, Wally's Walk,2113,Australia
3.Faculty of Geo-Information and Earth Observation (ITC),University of Twente,Enschede,Drienerlolaan 5,Netherlands
4.International Centre for Numerical Methods in Engineering,CIMNE,Barcelona,s/n, C/ Gran Capità, Catalunya,08034,Spain
5.Department of Earth and Space Sciences,Southern University of Science and Technology,Shenzhen,Guangdong,China

Burcet，Martí,Oliveira，Beñat,Afonso，Juan Carlos,et al. A face-centred finite volume approach for coupled transport phenomena and fluid flow[J]. Applied Mathematical Modelling,2024,125:293-312.

Burcet，Martí,Oliveira，Beñat,Afonso，Juan Carlos,&Zlotnik，Sergio.(2024).A face-centred finite volume approach for coupled transport phenomena and fluid flow.Applied Mathematical Modelling,125,293-312.

Burcet，Martí,et al."A face-centred finite volume approach for coupled transport phenomena and fluid flow".Applied Mathematical Modelling 125(2024):293-312.