A non symmetric FVM‐BEM coupling method

Abstract

We consider the prototype model for flow and transport of a concentration in porous media in an interior domain and couple it with a diffusion process in the corresponding unbounded exterior domain. To guarantee mass conservation and stability with respect to dominating convection also for a discrete solution we introduce a non symmetric coupling of the vertex‐centered finite volume method (FVM) and the boundary element method (BEM). BEM approximates the unbounded exterior problem which avoids truncation of the domain. One can also interpret that the (unbounded) exterior problem “replaces” the boundary conditions of the interior problem. We aim to provide a first rigorous analysis of the discrete system for different model parameters; existence and uniqueness, convergence, and a priori estimates. Numerical examples illustrate the strength of the chosen method which is computational cheaper than the previous three field FVM‐BEM couplings. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)