Gas Dynamics Equations: Computation

TL;DR

This paper reviews the development of numerical methods for computing weak entropy solutions of the Euler equations in gas dynamics, focusing on shock waves and wave interactions in supersonic flows.

Contribution

It discusses historic and recent advances, highlighting mathematical challenges in designing efficient algorithms for gas dynamics simulations.

Findings

Overview of numerical methods for shock wave computation

Discussion of mathematical challenges in weak entropy solutions

Insights into the evolution of computational techniques in gas dynamics

Abstract

Shock waves, vorticity waves, and entropy waves are fundamental discontinuity waves in nature and arise in supersonic or transonic gas flow, or from a very sudden release (explosion) of chemical, nuclear, electrical, radiation, or mechanical energy in a limited space. Tracking these discontinuities and their interactions, especially when and where new waves arise and interact in the motion of gases, is one of the main motivations for numerical computation for the gas dynamics equations. In this paper, we discuss some historic and recent developments, as well as mathematical challenges, in designing and formulating efficient numerical methods and algorithms to compute weak entropy solutions for the Euler equations for gas dynamics.