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.