Effective pressure interface law for transport phenomena between an unconfined fluid and a porous medium using homogenization

TL;DR

This paper rigorously derives the pressure jump condition at the interface between an unconfined fluid and a porous medium using homogenization, providing a theoretical foundation for previously numerically confirmed laws.

Contribution

It offers a rigorous derivation of the pressure interface law in coupled fluid-porous media flows via homogenization, extending prior numerical results.

Findings

Rigorous derivation of pressure jump condition

Validation of the interface law through boundary layer analysis

Extension of homogenization techniques to pressure interface modeling

Abstract

We present modeling of the incompressible viscous flows in the domain containing an unconfined fluid and a porous medium. For such setting a rigorous derivation of the Beavers-Joseph-Saffman interface condition was undertaken by J\"ager and Mikeli\'c [SIAM J. Appl. Math. \rm 60 (2000), p. 1111-1127] using the homogenization method. So far the interface law for the pressure was conceived and confirmed only numerically. In this article we justify rigorously the pressure jump condition using the corresponding boundary layer.