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A new numerical continuum \textit{one-domain} approach (ODA) solver ispresented for the simulation of the transfer processes between a free fluid anda porous medium. The solver is developed in the \textit{mesoscopic} scaleframework, where a continuous variation of the physical parameters of theporous medium (e.g., porosity and permeability) is assumed. TheNavier-Stokes-Brinkman equations are solved along with the continuity equation,under the hypothesis of incompressible fluid. The porous medium is assumed tobe fully saturated and can potentially be anisotropic. The domain isdiscretized with unstructured meshes allowing local refinements. A fractionaltime step procedure is applied, where one predictor and two corrector steps aresolved within each time iteration. The predictor step is solved in theframework of a marching in space and time procedure, with some importantnumerical advantages. The two corrector steps require the solution of largelinear systems, whose matrices are sparse, symmetric and positive definite,with $\mathcal{M}$-matrix property over Delaunay-meshes. A fast and efficientsolution is obtained using a preconditioned conjugate gradient method. Thediscretization adopted for the two corrector steps can be regarded as aTwo-Point-Flux-Approximation (TPFA) scheme, which, unlike the standard TPFAschemes, does not require the grid mesh to be $\mathbf{K}$-orthogonal, (with$\mathbf{K}$ the anisotropy tensor). As demonstrated with the provided testcases, the proposed scheme correctly retains the anisotropy effects within theporous medium. Furthermore, it overcomes the restrictions of existingmesoscopic scale one-domain approachs proposed in the literature.

A new numerical mesoscopic scale one-domain approach solver for free fluid/porous medium interaction