Abstract

Fully discrete bicompact schemes of the fourth order of approximation in space are investigated for entropy stability in problems of gas dynamics. Expressions for the rate of entropy production in these schemes are derived. Qualitative estimates are obtained for the behavior of this quantity. On the example of one-dimensional Riemann test problems, a numerical analysis of the entropy production rate for bicompact schemes of the first and third orders of approximation in time is carried out. From the results of this analysis, it is concluded whether any entropy correction is necessary for bicompact schemes.

中文翻译：

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气体动力学问题中双压缩方案的熵稳定性

摘要

针对气体动力学问题中的熵稳定性，研究了空间四阶近似的完全离散双紧凑方案。导出了这些方案中熵产生率的表达式。获得了该数量行为的定性估计。以一维黎曼检验问题为例，对时间上一阶和三阶近似的双紧方案的熵产生率进行了数值分析。根据该分析的结果，可以得出结论，双紧方案是否需要进行任何熵校正。