Extending the isoAdvector Geometric VOF Method to Flows in Porous Media

We consider the interfacial flow in and around porous structures in coastal and marine engineering.* During recent years, interfacial flow through porous media has been repeatedly simulated with Computational Fluid Dynamics (CFD) based on algebraic Volume Of Fluid (VOF) methods [1] [2]. Here, we present an implementation of a porous medium interfacial flow solver based on the geometric VOF method, isoAdvector [3] [4]. In our implementation, the porous medium is treated without resolving the actual pore geometry. Rather, the porous media, pores, and rigid structure are considered a continuum and the effects of porosity on the fluid flow are modelled through source terms in the Navier-Stokes equations, including Darcy-Forchheimer forces, added mass force and accounting for the part of mesh cells that are occupied by the solid material comprising the skeleton of the porous medium. The governing equations are adopted from the formulation by Jensen et al. [1]. For the interface advection using isoAdvector, we also account for the reduced cell volume available for fluid flow and for the increase in the interface front velocity caused by a cell being partially filled with solid material. The solver is implemented in the open source CFD library OpenFOAM®. It is validated using two case setups: 1) A pure passive advection test case to compare the isolated advection algorithm against a known analytical solution and 2) a porous dam break case by Liu et al. [5] where both numerical and experimental results are available for comparison. We find good agreement with numerical and experimental results. For both cases the interface sharpness, shape conservation as well as volume conservation and boundedness are demonstrated to be very good. The solver is released as open source for the benefit of the coastal and marine CFD community (code repository https://github.com/InterFlowers/porousInterIsoFoam) and as of OpenFOAM-v2112 the new functionality is integrated in the official interIsoFoam solver. * This article is an updated version of the conference paper Missios et al. 2022 [6] presented at the Marine2021 conference.