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