Numerical approach for incompressible fluid flows in and around a pair of porous elliptic cylinders

In this study we consider numerical simulations of incompressible fluid flow around and through a pair of porous/permeable elliptic cylinders. The mathematical model set up is based on Navier-Stokes (NS) equations in the free fluid domain Ω f together with convective Darcy-Brinkman-Forchheimer (CDBF) equations in the porous subdomains Ωp occupied by the two cylinders with an elliptical cross section. Continuity of velocity and stress boundary conditions are assumed at the interfaces separating the two fluid phases. Finite Element method based numerical approach is employed to study the two-dimensional flow problem. Numerical simulations are performed for various orientations of the ellipses. Results for different choices of the Reynolds number Re, the Darcy number Da, and nine orientations of the two ellipses are computed, demonstrating the efficacy of our ap-proach. The numerical solutions and simulations presented here are of some interest in modeling the filtration of incompressible fluids through non-circular porous inclusions.