Artificial viscosity: back to the basics

Abstract

SummaryIn this paper, we take a different perspective on the derivation of artificial viscosity. Heretofore, the development of artificial viscosity has been based on the paper published in Journal of Applied Physics in 1950 authored by John von Neumann and Robert Richtmyer [1]. Earlier, in 1948, Richtmyer published a report at Los Alamos Scientific Laboratory documenting the original concept [2]. This report was the true origin of shock capturing methods and contains several key ideas that are conceptually different than the 1950 journal article. Unfortunately, this report (LA‐671) was classified until 1993. This has resulted in two issues: the misattribution of the invention of artificial viscosity as primarily being the work of von Neumann and the loss of the structurally different ideas in the original report. We seek to right the record of history here and use the ideas contained in Richtmyer's report to good effect in deriving a new shock viscosity. The focus of previous development has been the Hugoniot curve describing the locus of states connected by a single shock wave. Here we follow a path more focused upon the Rayleigh line, which is strongly guided by Richtmyer's line of development of the original artificial viscosity formulation. We provide an implementation of the method resulting from this perspective and computational results for simple shock problems. Copyright © 2014 John Wiley & Sons, Ltd.