Study of the Effects of Artificial Dissipation and Other Numerical Parameters on Shock Wave Resolution

TL;DR

This study evaluates how different numerical schemes and parameters affect shock wave resolution in supersonic flows, highlighting the importance of artificial dissipation and scheme properties for accurate simulations.

Contribution

It introduces novel finite-difference interpretations of the AUSM+ scheme and compares their effectiveness in resolving shock waves in supersonic flows.

Findings

AUSM+ scheme variants improve shock resolution robustness.

Artificial dissipation reduces non-physical flow perturbations.

Good agreement with experimental data achieved.

Abstract

The effects induced by numerical schemes and mesh geometry on the solution of two-dimensional supersonic inviscid flows are investigated in the context of the compressible Euler equations. Five different finite-difference schemes are considered: the Beam and Warming implicit approximate factorization algorithm, the original Steger and Warming flux vector splitting algorithm, the van Leer approach on performing the flux vector splitting and two different novel finite-difference interpretations of the Liou AUSM+ scheme. Special focus is given to the shock wave resolution capabilities of each scheme for the solution of an external supersonic inviscid flows around a blunt body. Significant changes in the shock structure are observed, mainly due to special properties of the scheme in use and the influence of the domain transformation procedure. Perturbations in the supersonic flow upstream of the shock are also seen in the solution, which is a non-physical behavior. Freestream subtraction, flux limiting and the explicit addition of artificial dissipation are employed in order to circumvent these problems. One of the AUSM+ formulations presented here is seen to be particularly more robust in avoiding the appearance of some of these numerically-induced disturbances and non-physical characteristics in the solution. Good agreement is achieved with both numerical and experimental results available in the literature.}