Comparative Analysis of Obstacle Approximation Strategies for the Steady Incompressible Navier-Stokes Equations

This paper aims to compare and evaluate various obstacle approximation techniques employed in the context of the steady incompressible Navier-Stokes equations. Specifically, we investigate the effectiveness of a standard volume penalization approximation and an approximation method utilizing high viscosity inside the obstacle region, as well as their composition. Analytical results concerning the convergence rate of these approaches are provided, and extensive numerical experiments are conducted to validate their performance.