A thermodynamically consistent numerical method for transonic cascade flow simulation

The author's recent work on thermodynamically consistent numerical methods for the simulation of inviscid, adiabatic flow is extended to handle transonic flow problems of practical interest. The basic Singhal–Spalding scheme is developed and tested on two problems. The first one is the standard transonic nozzle flow. The computational results are shown to be in good agreement with the analytical solution. The second problem is a flow situation studied experimentlly by Sieverding. The inviscid results are in surprisingly good agreement with the principal qualitative features of the real folws. There are important quantitative discrepancies which are believed to be due to the inadequacies of the inviscid model rather than failings of the scheme itself. Arguments in support for this view are presented.