Shock modelling in transonic and supersonic flow

Numerical simulation studies of problems in transonic flow are conducted in connection with the design of aircraft flying near the speed of sound, while recently there has also been a great deal of interest in supersonic and hypersonic flow calculations. Three important models for inviscid compressible gasdynamics are utilized in the study of these flow problems, taking into account the transonic small disturbance equation (TSD), the transonic full potential equation (FP), and the full Euler equations for compressible gasdynamics (EU). The present paper has the objective to provide a description of shock capturing methods recently developed for each model. The design principles behind the algorithms are also examined, giving attention to consistency, conservative form, monotone and sharp discrete shocks, and a bound on the variation, which prevents spurious oscillations.