Mixed Dirichlet–Robin problem for coupled anisotropic Navier–Stokes-type systems

This paper is concerned with the analysis of mixed Dirichlet–Robin boundary value problems for the anisotropic Brinkman and Darcy–Forchheimer–Brinkman systems, as well as a system of d ≥ 1 d ≥ 1 coupled anisotropic Darcy–Forchheimer–Brinkman equations in bounded Lipschitz domains in Rⁿ, n = 2,3 R n , n = 2 , 3 . These systems provide general models for flows of anisotropic viscous incompressible fluids in heterogeneous and multidisperse porous media. By combining a variational approach and fixed-point techniques, we establish the existence and uniqueness of weak solutions in L²- L 2 - based Sobolev spaces under suitable smallness conditions on the given data. To demonstrate the applicability of the theoretical results, we carry out a numerical investigation of the lid-driven flow problem in a square monodisperse or bidisperse porous cavity containing a solid circular obstacle, employing a Robin boundary condition on the moving lid and examining the effect of key physical parameters on the flow behavior.