Year: 2026
Type: article
Abstract: 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 $$d \ge 1$$ d ≥ 1 coupled anisotropic Darcy–Forchheimer–Brinkman equations in bounded Lipschitz domains in $$\mathbb {R}^n, n = 2,3$$ 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 $$\textrm{L}^2-$$ 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.
Author: Andrei Gasparovici
Institution: Babeș-Bolyai University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,590
OpenAlex ID: W7154499546