High-order finite-difference implementation of the immersed-boundary technique for incompressible flows

A high-resolution, two-dimensional (2-D), vortex particle method is implemented, and simulations of flows around various bluff bodies are presented, with a detailed analysis of the flow around rectangular cylinders. Long-time simulations of flows around square and rectangular cylinders at low to moderate Reynolds numbers are then performed, and the resulting Strouhal–Reynolds number relationships are compared with experimental and numerical data in the literature. The well-known stepwise variation of the chord-based Strouhal number with chord-to-thickness ratio for rectangular cylinders is replicated, and the flow field is explored and compared with experimental observations. Further analyses with identified vortices provide new insights into the shedding process that leads to the stepwise variation of chord-based Strouhal numbers and the frequency jumps.