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.

翻译：超声速或高超声速流动的数值模拟中，若流场包含强激波，常出现数值激波不稳定性问题，限制了激波捕捉格式的进一步应用。本文针对三模板格式发展了统一矩阵稳定性分析方法，并开发了开源工具MSAT，用于定量分析激波不稳定性问题。基于结构化网格的有限体积方法，MSAT可用于研究激波不稳定性问题的机理、评估数值格式的鲁棒性，进而辅助发展鲁棒格式。此外，MSAT具备分析实际超声速或高超声速流动模拟的能力，可评估其是否会出现激波不稳定性，并据此协助选择适当的数值格式。因此，MSAT是研究激波不稳定性问题并帮助消除该问题的有效工具。