Coupling staggered-grid and vertex-centered finite-volume methods for coupled porous-medium free-flow problems

TL;DR

This paper introduces a novel discretization method combining staggered-grid and vertex-centered finite volume techniques for coupled free-flow and porous-medium problems, enabling flexible grid use and accurate interface coupling.

Contribution

The paper presents a new coupled discretization approach that handles non-matching grids and complex interface conditions in free and porous medium flows.

Findings

Method achieves convergence across various grid types.

Accurate coupling of flow conditions at interfaces.

Successfully incorporates nonlinear velocity-dependent terms.

Abstract

In this work, a new discretization approach for coupled free and porous-medium flows is introduced, which uses a finite volume staggered-grid method for the discretization of the Navier-Stokes equations in the free-flow subdomain, while a vertex-centered finite volume method is used in the porous-medium flow domain. The latter allows for the use of unstructured grids in the porous-medium subdomain, and the presented method is capable of handling non-matching grids at the interface. In addition, the accurate evaluation of coupling terms and of additional nonlinear velocity-dependent terms in the porous medium is ensured by the use of basis functions and by having degrees of freedom naturally located at the interface. The available advantages of this coupling method are investigated in a series of tests: a convergence test for various grid types, an evaluation of the implementation of coupling conditions, and an example using the velocity dependent Forchheimer term in the porous-medium subdomain.