MSAT: Matrix stability analysis tool for shock-capturing schemes

TL;DR

This paper introduces MSAT, an open-source matrix stability analysis tool designed to diagnose and mitigate shock instabilities in shock-capturing schemes for supersonic and hypersonic flow simulations.

Contribution

The paper develops a unified matrix stability analysis method and presents MSAT, a tool for analyzing, understanding, and improving the robustness of shock-capturing numerical schemes.

Findings

MSAT can effectively analyze shock instability mechanisms.

MSAT helps evaluate the robustness of different numerical schemes.

MSAT assists in selecting suitable schemes for high-speed flow simulations.

Abstract

The simulation of supersonic or hypersonic flows often suffers from numerical shock instabilities if the flow field contains strong shocks, limiting the further application of shock-capturing schemes. In this paper, we develop the unified matrix stability analysis method for schemes with three-point stencils and present MSAT, an open-source tool to quantitatively analyze the shock instability problem. Based on the finite-volume approach on the structured grid, MSAT can be employed to investigate the mechanism of the shock instability problem, evaluate the robustness of numerical schemes, and then help to develop robust schemes. Also, MSAT has the ability to analyze the practical simulation of supersonic or hypersonic flows, evaluate whether it will suffer from shock instabilities, and then assist in selecting appropriate numerical schemes accordingly. As a result, MSAT is a helpful tool that can investigate the shock instability problem and help to cure it.