Comparison between direct numerical simulations and effective models for fluid-porous flows using penalization

This work is devoted to a numerical study of two-dimensional incompressible flows in a fluid-porous medium system placed on an impermeable wall. Flow in the whole system is studied either at the pore scale or at the Darcy scale (using a one-domain approach) and the models at both scales are solved with a penalization method using the same formal Navier-Stokes equations modified by a Darcy-like term. Several effective medium penalized models are considered for the simulations. Various flow regimes are investigated ranging from laminar to turbulent. The velocity profiles inside and outside the porous medium show significant discrepancies between the different penalization models compared to the direct numerical simulations. This work motivates further studies about the spatial variations of the penalization coefficient to be introduced in the effective medium models in order to better reproduce the physics near the fluid-porous medium boundaries.