Numerical study of flow in a lid-driven cavity with internal square obstacle using FEM

This study numerically investigates lid-driven flow in a square cavity containing centrally located square obstacles of varying sizes, using the finite element method implemented in COMSOL Multiphysics. In contrast to previous research that predominantly addressed circular obstacles, this work focuses on the unique effects introduced by sharp-edged, square barriers on the flow structure. Grid independence was verified up to a [Formula: see text] mesh, with simulations presented on a fine [Formula: see text] grid across a wide Reynolds number range (100–5000). The results demonstrate excellent agreement with benchmark solutions, including those from the lattice Boltzmann method, confirming the reliability of the numerical approach. As the Reynolds number increases, the main vortex migrates toward the cavity center, while the influence of secondary vortices near the obstacles diminishes. Additionally, the presence and size of square obstacles characterized by side-to-cavity length ratios from [Formula: see text] to [Formula: see text] substantially modify the formation and strength of corner vortices. The sharp geometry of square obstacles induces distinct flow separation patterns compared to traditional circular forms, leading to pronounced changes in vortex dynamics. These insights advance the understanding of internal geometry effects in lid-driven cavity flows, with practical implications for the design of compact thermal-fluid systems such as microfluidic devices and heat exchangers.