MSAT: Matrix stability analysis tool for shock-capturing schemes

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.