A Stress Mapping Immersed Boundary Method for Viscous Flows

This work introduces an immersed boundary method for two-dimensional simulation of incompressible Navier-Stokes equations. The method uses flow field mapping on the immersed boundary and performs a contour integration to calculate immersed boundary forces. This takes into account the relative location of the immersed boundary inside the background grid elements by using inverse distance weights, and also considers the curvature of the immersed boundary edges. The governing equations of the fluid mechanics are solved using a Galerkin-Least squares finite element formulation. The model is validated against a stationary and a vertically oscillating circular cylinder in a cross flow. The results of the model show acceptable accuracy when compared to experimental and numerical results.