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：本文针对可压缩流动方程提出了一组兼具动能保持、压力平衡保持及渐近熵守恒特性的数值通量，即该类通量能够任意降低因空间离散导致的熵产生数值误差。这些通量基于内能的调和平均构造且仅依赖代数运算，相较于基于对数平均的熵守恒通量具有更低的计算成本。研究进一步探索了几何平均的适用性，证实其能有效降低熵演化误差。数值试验结果验证了理论预测，并对所选格式的熵守恒性能进行了比较分析。