# Coupling Staggered-Grid and MPFA Finite Volume Methods for Free Flow/Porous-Medium Flow Problems

## TL;DR

This paper introduces a coupled discretization method combining staggered-grid and MPFA finite volume techniques to accurately simulate free flow and anisotropic porous medium flow, ensuring stability and good agreement with existing methods.

## Contribution

It presents a novel coupling scheme that integrates staggered-grid and MPFA finite volume methods for improved modeling of free flow and anisotropic porous media.

## Key findings

- Stable and applicable in anisotropic conditions
- Enhanced accuracy near porous medium boundaries
- Good agreement with existing models

## Abstract

A discretization is proposed for models coupling free flow with anisotropic porous medium flow. Our approach employs a staggered grid finite volume method for the Navier-Stokes equations in the free flow subdomain and a MPFA finite volume method to solve Darcy flow in the porous medium. After appropriate spatial refinement in the free flow domain, the degrees of freedom are conveniently located to allow for a natural coupling of the two discretization schemes. In turn, we automatically obtain a more accurate description of the flow field surrounding the porous medium. Numerical experiments highlight the stability and applicability of the scheme in the presence of anisotropy and show good agreement with existing methods, verifying our approach.