Simulation of vortex shedding flows using high-order fractional step methods

Abstract

Unsteady flow past a square cylinder is simulated using a fractional step method to advance the Navier-Stokes equations in time. The fractional step method is a single step method whereby the momentum equations are solved using an explicit/implicit scheme and an approximate pressure field to yield an estimate of the velocity. This velocity is then projected onto a divergence free field using a pressure correction obtained by the solution of a Poisson pressure correction equation. The integration then proceeds to the next time step. Results were obtained using a Crank-Nicolson scheme and hybrid second and third order Adams-Bashforth/Adams-Moulton schemes and second order in time behaviour is verified for velocities for a developed flow over a square cylinder. Results will be presented comparing the accuracy and efficiency of these schemes with unsteady flows of this type, as well as detailing some of the pitfalls that can be encountered with this approach.