Finite element implementation of stress-jump and stress-continuity conditions at porous-medium, clear-fluid interface

The boundary conditions at the interface between clear-fluid and porous-medium domains are very important for solving flow through an open domain adjoining a porous medium. In this Galerkin finite-element (FE) based simulation of such interface flows employing Stokes and Brinkman equations, the traditional interfacial condition based on the continuity of stress in fluid and porous media is compared with the stress-jump condition proposed by Ochoa-Tapia and Whitaker using the rigorous volume averaging method. A novel FE formulation employing a second-order adjustable tensor is proposed to implement this new stress-jump condition for full three-dimensional flows. The paper also clarifies the hitherto obscure relationship between flow variables in the fluid and porous media for the conventional stress-continuity condition. In the first validation study involving numerical predictions of flow parallel to the interface, our FE implementation of the new stress-jump condition agree very well with the analytical solution for flow parallel to the interface, thereby proving the soundness of our adjustable tensor approach. Similar excellent results were obtained for FE implementation of the stress-continuity condition as well. A good match with analytical solution for a constant cross-flow superimposed on the parallel flow was also achieved while differences in velocity profiles near the interfaces were studied for the two conditions. Lastly a complex 3D flow simulation involving a fluid and porous media interface within the unit-cell of a non-crimp stitched fiber mat, used in liquid composite molding process during the manufacture of composite materials, is undertaken. The permeability of this dual-scale fibrous porous medium, estimated using the newly implemented stress-jump condition, agrees well with the experimental result thereby pointing to the accuracy of the FE implementation of the condition. Our simulations reveal that the stress-jump condition leads to a much smaller boundary layer within porous medium near the interface as compared to the stress-continuity condition, and hence to a lower, more accurate net flow-rate through the unit cell. However the two interfacial conditions yield similar results with a decrease in the porosity.