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.

在本文中，进行了持续的研究，以探索强冲击的 Godunov 型方案的数值冲击不稳定性的潜在机制。通过对 Godunov 型方案的耗散分析和一系列数值实验，我们能够阐明不稳定可能归因于数值激波结构内部的熵产生不足。因此，开发了一种通用的熵控制技术，用于提高各种 Godunov 型方案在强冲击下的鲁棒性。它起到了保证在数值激波结构内部产生足够熵的作用。此外，这种改进的方法不会在线性退化波上引入任何额外的数值耗散来抑制冲击不稳定性。