Random Choice Method on a Non-Staggered Grid Utilising an Efficient Riemann Solver

摘要

A practical description of the random choice method (RCM) on non-staggered grids is presented. The original idea appears to be due to Colella (1982). The approach is much simpler than the staggered grid version of RCM traditionally used. It also offers a number of advantages with regard to the use of non-regular meshes in space and time, adaptive gridding and hybridization of RCM with other methods. Also an exact Riemann solver is presented that is shown to be very efficient and simple to use. Its performance is comparable to the method of Gottlieb (1986) and significantly faster than the approximate Riemann solver of Dukowicz (1985), at least for the ideal equation of state considered here.