A non-symmetric coupling of the finite volume method and the boundary element method

TL;DR

This paper introduces a novel non-symmetric coupling of finite volume and boundary element methods for flow and transport problems, providing stability, conservation, and convergence analysis with numerical validation.

Contribution

It develops a new non-symmetric coupling approach for finite volume and boundary element methods, including stability and convergence analysis for porous media flow models.

Findings

The coupling preserves local flux conservation.

The method is stable in convection-dominated regimes.

Numerical experiments confirm theoretical stability and convergence.

Abstract

As model problem we consider the prototype 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 solve the problem we develop a new non-symmetric coupling between the vertex-centered finite volume and boundary element method. This discretization provides naturally conservation of local fluxes and with an upwind option also stability in the convection dominated case. We aim to provide a first rigorous analysis of the system for different model parameters; stability, convergence, and a~priori estimates. This includes the use of an implicit stabilization, known from the finite element and boundary element method coupling. Some numerical experiments conclude the work and confirm the theoretical results.