Calculation of supersonic steady-state flow in axisymmetric nozzles with an upwind difference scheme

This paper is on the application of the upwind difference scheme proposed by the author^[1] to the calculation of supersonic steady-state flow in axisymmetric nozzles. The upwind scheme is conservative (or weakly conservative), it yields results approximating those from the characteristic relations, and it has corresponding boundary difference schemes. The entropy phenomenon in the calculation of shock reflection on boundaries with the shock-capturing method will be discussed and a correction of this phenomenon will be proposed. From numerical experiments on an arbitrary nozzle, it is seen that the upwind difference scheme, its corresponding boundary scheme, and the improved treatment of shock reflection work well for the calculation of supersonic steady-state flow in axisymmetric nozzles.