Stabilized Finite Element Approximation for The Transient Darcy-Brinkman-Forchheimer Model

This work presents a robust stabilized finite element solution for the Darcy-Brinkman-Forchheimer model, addressing transient incompressible flow within a porous medium. The approach employs the finite element Galerkin method, complemented by stabilization terms from Streamline-Upwind/Petrov-Galerkin (SUPG) and Pressure-Stabilizing/Petrov-Galerkin (PSPG). Equal-order linear triangular finite elements were used, and due to the nonlinear characteristic of the problem, for the solution procedure, the predictor multi-corrector algorithm was employed. Synthetic problems, serving as benchmarks, were formulated and equipped with fabricated analytical solutions to verify our proposed solutions. The study contributes to understanding the application of those techniques in the computational treatment of fluid flow problems in porous medium. The utilization of synthetic problems with known analytical solutions enhances the confidence in the accuracy and reliability of our proposed finite element solution.