Solution of Navier-Stokes equations on nonstaggered grid at all speeds

The present author recently devised a pressure correction algorithm for solution of incompressible Navier-Stokes equations on a nonstaggered grid [6]. This algorithm introduced the notion of smoothing pressure correction to overcome the problem of checkerboard prediction of pressure. In this article, the algorithm is extended to prediction of compressible flows with and without shocks. The predictions show that the algorithm yields results that compare extremely favorably with previous ones [2] obtained using a staggered grid. Accurate shock capturing on coarse grids, however, requires use of total variation diminishing (TVD) discretization of the covective terms coupled with measures for stabilization of the iteration process