A hybrid-dimensional Stokes-Brinkman-Darcy model for arbitrary flows to the fluid-porous interface

Abstract

Mathematical modelling of coupled flow systems containing a free-flow region in contact with a porous medium is challenging, especially for arbitrary flow directions to the fluid-porous interface. Transport processes in the free flow and porous medium are typically described by distinct equations: the Stokes equations and Darcy’s law, respectively, with an appropriate set of coupling conditions at the common interface. Classical interface conditions based on the Beavers-Joseph condition are not accurate for general flows. Several generalisations are recently developed for arbitrary flows at the interface; some of them are however only theoretically formulated and still need to be validated. In this manuscript, we propose an alternative to couple free flow and porous-medium flow, namely the hybrid-dimensional Stokes-Brinkman-Darcy model. Such formulation incorporates the averaged Brinkman equations within a complex interface between the free-flow and porous-medium regions. The complex interface acts as a buffer zone facilitating storage and transport of mass and momentum and the model is applicable for arbitrary flow directions. We validate the proposed hybrid-dimensional model against the pore-scale resolved model in multiple examples and compare numerical simulation results also with the classical and generalised coupling conditions from the literature. The proposed hybrid-dimensional model demonstrates its applicability to describe arbitrary coupled flows and shows its advantages in comparison to other generalised coupling conditions.