A conservative finite difference method and its application for the analysis of a transient flow around a square prism

Detailed results of numerical calculations of transient, 2D incompressible flow around and in the wake of a square prism at Re = 100, 200 and 500 are presented. An implicit finite difference operator-splitting method, a versi on of the known SIMPLEC-like method an a staggered grid, is described. Appr opriate theoretical results are presented The method has second-order accur acy in space, conserving mass, momentum and Kinetic energy. A new modificat ion of the multigrid method is employed to salve the elliptic pressure prob lem. Calculations are performed on a sequence of spatial grids with up to 4 01 x 321 grid points, at sequentially halved time steps to ensure grid-inde pendent results. Three types of flow are shown to exist at Re = 500: a stea dy-state unstable flow and two which are transient, fully periodic and asym metric about the centre fine but mirror symmetric to each other Discrete fr equency spectra of drag and lift coefficients ave presented.