A non-symmetric coupling of the finite volume method and the boundary element method
For researchers in computational fluid dynamics and porous media, this offers a new coupling approach with conservation properties, though it is an incremental extension of existing coupling techniques.
The paper develops a non-symmetric coupling of the finite volume method and boundary element method for flow and transport in porous media, providing rigorous stability and convergence analysis with numerical validation.
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.