Reflections on the early development of the “AUSM family” of Riemann solvers

Abstract

This paper is written in honor and memory of my esteemed friend and colleague, Meng-Sing Liou, with whom I worked closely in the 1990s on the development of AUSM-family schemes and their extensions to reactive, “all-speed,” and multi-phase flows. The purpose of this paper is to revisit the thought processes and concepts that led to the rapid evolution of the AUSM family as a highly efficient, highly accurate method for discretization of the Euler equations and their various extensions. No new results are presented; rather, the focus is on (re-)discovering the common threads that link the various members of the AUSM family. Special attention is given to the strategies that lead to accurate results at all flow speeds, and some reviews of more current work in this area are presented. The paper concludes with a few reflections, personal and otherwise, relating to my interactions with Meng over the years and to my view of the essential elements of AUSM-family schemes.