A flux splitting method for the Euler equations

Abstract

The solution of the Euler and Navier–Stokes equations was the focus of this research. As with methods such as the AUSM-family, this work further attempted to construct an explicit upwind method that combines both simplicity and accuracy. In particular, with an appropriate choice of working variables, the aim was to develop a simple method that is based on the advection of the characteristic variables. The end result is a computationally efficient method valid for all homogeneous fluids with accuracy comparable to that of expensive flux-difference splitting methods. Good performance was extensively verified with Riemann test problems and results were on par with Roe’s scheme. Furthermore, at least one formulation of the method passed all test problems satisfactory without requiring manual intervention. The method also illuminates some similarities between flux-difference splitting and the AUSM-family of methods