Version [1.1]—[MSAT: Matrix stability analysis tool for shock-capturing schemes]

Abstract

The numerical shock instability problem significantly limits the application of the finite volume method in hypersonic flow simulations, especially for high-order schemes, which will encounter more severe shock instability problems. In the previous work, the MSAT (matrix stability analysis tool) was introduced to quantitatively analyze the numerical shock instability problem. However, the utilization of the three-point reconstruction stencil in the original version of MSAT presents challenges in conducting investigations into high-order schemes. The current work provides an extension of MSAT by extending the reconstruction stencil to five points, a challenging but necessary endeavor for high-order schemes. This extension enables MSAT to provide analyses for schemes with high-order reconstruction methods. Furthermore, the updated MSAT can be utilized to investigate the impact of characteristic variable reconstruction on the shock instability problem. Results demonstrate the reliability of the updated MSAT and reveal novel characteristics in the shock instability of high-order schemes. Consequently, the updated MSAT will contribute to the investigation of shock instabilities for high-order schemes, ultimately aiding in mitigating this challenging problem.