Coupling Staggered-Grid and MPFA Finite Volume Methods for Free Flow/Porous-Medium Flow Problems
This work provides a numerical scheme for engineers and scientists modeling coupled free and porous media flow, but it is an incremental combination of existing methods.
The paper proposes a coupling of staggered-grid and MPFA finite volume methods for free flow/porous-medium flow problems, achieving stability and accuracy in anisotropic cases, with good agreement to existing methods.
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.