This paper proposes a hierarchy of numerical fluxes for the compressible flow equations which are kinetic-energy and pressure equilibrium preserving and asymptotically entropy conservative, i.e., they are able to arbitrarily reduce the numerical error on entropy production due to the spatial discretization. The fluxes are based on the use of the harmonic mean for internal energy and only use algebraic operations, making them less computationally expensive than the entropy-conserving fluxes based on the logarithmic mean. The use of the geometric mean is also explored and identified to be well-suited to reduce errors on entropy evolution. Results of numerical tests confirmed the theoretical predictions and the entropy-conserving capabilities of a selection of schemes have been compared.

翻译：本文提出了一组适用于可压缩流动方程的数值通量，这些通量具有保持动能和压力平衡以及渐近熵守恒的特性，即它们能够任意减小由于空间离散化而产生的熵生成数值误差。该通量基于内能调和平均的使用，仅涉及代数运算，因此比基于对数平均的熵守恒通量计算成本更低。本文还探讨了几何平均的应用，并发现其适用于减少熵演化中的误差。数值测试结果验证了理论预测，并对所选方案在熵守恒能力方面进行了比较。