A pure Stokes approach for coupling fluid flow with porous media flow.

Most numerical approaches for coupling fluid flow with porous media flow rely either on Stokes equations in the fluid part of the domain and Darcy's law in the porous part, or on Brinkman's equation. In both cases, difficulties arise at the boundary between the two parts because the equations used in the porous part are not of Stokes type. In this paper, an alternative to Darcy's law is proposed for modeling flows in porous media. This alternative relies on equations of Stokes type where the permeability tensor is replaced by force and stress derivative tensors. Numerical procedures are presented to compute these tensors from simulations at pore scale. Simulations in domains containing both fluid and porous parts are finally conducted simply assuming continuity of velocity and pressure and hence without imposing any condition at the boundary between the two parts. Results show that the proposed method is accurate and hence a promising alternative to Darcy's law for problems involving both fluid and porous parts. • Alternative to Darcy's law relying on equations of Stokes type for modeling flows in porous media. • Permeability tensor replaced by force and stress derivatives tensors computed from simulations at pore scale. • Flows in domains containing both fluid and porous parts modeled without any boundary conditions between the two parts. [ABSTRACT FROM AUTHOR]