On a Dirichlet problem for the Darcy-Forchheimer-Brinkman system with application to lid-driven porous cavity flow with internal square block

Abstract

In this paper we are concerned with both theoretical and numerical study of a Dirichlet boundary value problem for the nonlinear Darcy-Forchheimer-Brinkman system on a bounded Lipschitz domain in Rn(n=2,3). Using the potential theory technique we obtain a well-posed theorem which implies the existence and uniqueness of a weak solution for the aforementioned Dirichlet problem when the boundary data belongs to a L2-based Sobolev space. A numerical investigation of the flow of a viscous fluid through a two dimensional lid-driven porous cavity with a solid square block is performed. The effect of the dimension and position of the internal obstacle on the flow behaviour is analysed.