Comparative study of numerical schemes for strong shock simulation using the Euler equations

Abstract

A numerical study of extremely strong shocks was presented. Various types of numerical schemes with first-order accuracy and higher- order accuracy with adaptive stencils were implemented to solve the one and two-dimensional Euler equations based on the explicit finite difference method, including Roe’s first-order upwind, Steger-Warming Flux Vector splitting (FVS), Sweby’s flux-limited and Essentially Non-oscillatory (ENO) scheme. The result comparisons were carried out to discuss which scheme is the most suitable for strong shock problem. The dissipative nature of the first-order scheme can be easily seen from the numerical solutions. High order ENO scheme had the best resolution for the case having weak discontinuity, but it over- predicted the shock wave location for the case of strong discontinuity.