The relation between flux vector splitting and parabolized schemes

Abstract

The relationship between PNS and thin layer Navier-Stokes algorithms is used to develop traditional as well as new PNS procedures. The use of characteristics-based flux vector splitting gives rise to a parabolized system that is based on the predominant physics of the flow, while pressure-gradient-based flux vector splitting is shown to give the traditional parabolized scheme of Vigneron. Comparisons with TLNS results show the characteristics-based PNS system gives results that are at least as accurate as the more traditional pressure-gradient-split PNS system. The use of a safety factor in the pressure-gradient splitting is shown to cause inaccuracies and should be avoided. The interpretation of PNS procedures as the first sweep of a TLNS ADI procedure also suggests an obvious global pressure iteration method that is mathematically well posed and, hence, leads to an efficient rapidly converging global iteration procedure.