Shock capturing using a pressure-correction method

Abstract

A new pressure-correction scheme has been developed, which is suitable for the calculation of a flow containing a wide range of Mach numbers such as a transonic impinging jet. The method uses equations based on properties per unit volume so that momentum is retained as a basic dependent variable rather than velocity. This simplifies the discretization of the time-dependent flow equations and allows a direct relationship to be determined between pressure and mass flux. The hyperbolic nature of the system of equations is obtained by using the retarded pressure approach. This is a transformation of the real pressure based on local Mach number and is used in the momentum and pressure-correction equations. The shocked quasi-one-dimensional flow in a nozzle is used as a test of shock capturing properties and speed of computation. The new method gives precise shock capturing over two nodes with no over or under-shoots; it is also significantly faster than the MacCormack and Jameson explicit schemes tested for this problem. Finally, a turbulent, under-expanded, axisymmetric, impinging jet calculation is presented. The correct periodic under/over-expansions of the jet are predicted, and the normal standoff shock is cleanly captured.