Generalised coupling conditions for flows arbitrary to the fluid-porous interface: Development, vali

Presented by Elissa Eggenweiler (Stuttgart University)

Abstract: Physically consistent interface conditions are important for accurate mathematical modelling and numerical simulation of flow and transport processes in coupled free-flow and porous-medium systems. Classical coupling conditions are only valid for uni-directional flows, parallel or perpendicular to the fluid-porous interface. Alternative interface conditions either contain model parameters, which still need to be determined, or they are not validated for arbitrary flows to the porous layer. These restrictions severely limit the range of applications, which can be accurately modelled. Therefore, generalised interface conditions are necessary.

In this talk, we present new, generalised coupling conditions for the Stokes-Darcy problem. These conditions are rigorously derived using homogenisation and boundary layer theory and are valid for arbitrary flow directions. We validate the proposed conditions numerically by comparison of pore-scale to macroscale simulation results and demonstrate the advantages of the new conditions over the classical ones. We also prove the well-posedness of the coupled Stokes-Darcy problem with the derived interface conditions.