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Speed of Sound and Real Gas Solution Algorithm for Supercritical Flows

机译：超临界流的声速和真气速度求解算法

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摘要

The definition of the speed of sound is reexamined since it is crucial in the numerical analysis of compressible real gas flows. The thermodynamic speed of sound (TSS), a_(th), and the characteristic speed of sound (CSS), a_(ch), are derived using generalized equation of state (EOS). It is found that the real gas EOS, for which pressure is not linearly dependent on density and temperature, results in slightly different TSS and CSS. in this formalism, Roe's approximate Riemann solver was derived again with corrections for real gases. The results show a little difference when the speeds of sound are applied to the Roe's scheme and Advection Upstream Splitting Method (AUSM) scheme, but a numerical instability is observed for a special case using AUSM scheme. It is considered reasonable to use of CSS for the mathematical consistency of the numerical schemes. The approach is applicable to multi-dimensional problems consistently.
机译：声音速度的定义被重新检查，因为它在可压缩真实气流的数值分析中至关重要。使用广义状态方程（EOS）导出声音的热力学速度（TSS）a_（th）和特征声音速度（CSS）a_（ch）。已经发现，压力不线性依赖于密度和温度的实际气体EOS会导致TSS和CSS略有不同。在这种形式主义中，通过对真实气体的修正，再次推导了Roe的近似Riemann解算器。当将声速应用于Roe方案和对流上游分裂方法（AUSM）方案时，结果显示出一点点差异，但是在使用AUSM方案的特殊情况下，观察到数值不稳定。对于数值方案的数学一致性，使用CSS被认为是合理的。该方法始终如一地适用于多维问题。

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