Ключевое слово: «fenics.»

The classical darcy model is insufficient for describing high-velocity filtration flows where inertial and viscous effects are significant. This paper presents a numerical comparison of the darcy, darcy-forchheimer, and the comprehensive darcy-forchheimer-brinkman models to quantify the impact of these phenomena. Using the finite element method with picard iteration, we simulate flow in a simple square domain. The results clearly show that the forchheimer inertial term introduces a non-linear pressure drop, while the brinkman viscous term smooths the velocity field by resolving viscous stresses. This study provides a clear numerical benchmark, highlighting the critical conditions under which each physical effect becomes dominant and underscoring the importance of model selection for accurate predictions in applications ranging from petroleum engineering to biomechanics.