Fast estimation from above of the maximum wave speed in the Riemann problem for the Euler equations

TL;DR

This paper introduces a rapid, cubic-converging algorithm for estimating the maximum wave speed in the Riemann problem for Euler equations with co-volume gas, providing guaranteed upper bounds with prescribed accuracy.

Contribution

The paper presents a novel, fast algorithm that guarantees an upper bound on the maximum wave speed with cubic convergence for gases with specific equations of state.

Findings

Algorithm achieves cubic convergence rate.

Provides guaranteed upper bounds for wave speed.

Applicable to gases with co-volume equation of state and specific gamma range.

Abstract

This paper is concerned with the construction of a fast algorithm for computing the maximum speed of propagation in the Riemann solution for the Euler system of gas dynamics with the co-volume equation of state. The novelty in the algorithm is that it stops when a guaranteed upper bound for the maximum speed is reached with a prescribed accuracy. The convergence rate of the algorithm is cubic and the bound is guaranteed for gasses with the co-volume equation of state and the heat capacity ratio $\gamma$ in the range $(1,5/3]$