# Further studies on numerical instabilities of Godunov-type schemes for strong shocks

## TL;DR

This paper investigates the causes of numerical shock instabilities in Godunov-type schemes for strong shocks and proposes an entropy-control technique to enhance their robustness without sacrificing accuracy.

## Contribution

It introduces a general entropy-control method that improves the stability of Godunov-type schemes at strong shocks by ensuring sufficient entropy production inside the shock structure.

## Key findings

- The instability is linked to insufficient entropy production.
- The proposed entropy-control technique enhances robustness.
- Numerical tests confirm improved accuracy and stability.

## Abstract

In this paper, continuous research is undertaken to explore the underlying mechanism of numerical shock instabilities of Godunov-type schemes for strong shocks. By conducting dissipation analysis of Godunov-type schemes and a sequence of numerical experiments, we are able to clarify that the instability may be attributed to insufficient entropy production inside the numerical shock structure. As a result, a general entropy-control technique for improving the robustness of various Godunov-type schemes at strong shocks is developed. It plays a part in guaranteeing that enough entropy is produced inside the numerical shock structure. Furthermore, such a modified approach does not introduce any additional numerical dissipation on linear degenerate waves to suppress the shock instability. Numerical results that are obtained for various test cases indicate that the proposed methods have a good performance in terms of accuracy and robustness.