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Solving the advection–dispersion equation with discontinuous Galerkin and multipoint flux approximation methods on unstructured meshes
Author(s) -
Younes Anis,
Ackerer Philippe
Publication year - 2008
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1783
Subject(s) - discretization , advection , polygon mesh , discontinuous galerkin method , mathematics , finite element method , convection–diffusion equation , upwind scheme , dispersion (optics) , flux (metallurgy) , mathematical analysis , geometry , physics , materials science , optics , metallurgy , thermodynamics
In this work, we develop a new model to solve the advection–dispersion transport equation on unstructured triangular meshes. The model combines numerical methods that are specifically suited to achieve high accuracy for each type of equation without using the time splitting procedure. It is based on a combination of the upwind discontinuous Galerkin (DG) method for advection and the multipoint flux approximation (MPFA) method for dispersion. In contrast to mixed finite elements, MPFA methods provide fluxes at element interfaces explicitly by weighted sums of discrete element concentrations. Therefore, the combination of DG and MPFA methods allows taking into account total flux boundary conditions while using different numerical techniques. A theta‐scheme time discretization is developed for advection and an implicit scheme for dispersion. Accuracy of the numerical model is shown by simulating (i) the transport of a tracer in a simplified bidimensional problem with highly unstructured mesh and (ii) a laboratory‐scale experiment with high viscosity contrasts. Copyright © 2008 John Wiley & Sons, Ltd.