This work presents a procedure to solve the Euler equations by explicitly updating, in a conservative manner, a generic thermodynamic variable such as temperature, pressure or entropy instead of the total energy. The presented procedure is valid for any equation of state and spatial discretization. When using complex equations of state such as Span-Wagner, choosing the temperature as the generic thermodynamic variable yields great reductions in the computational costs associated to thermodynamic evaluations. Results computed with a state of the art thermodynamic model are presented, and computational times are analyzed. Particular attention is dedicated to the conservation of total energy, the propagation speed of shock waves and jump conditions. The procedure is thoroughly tested using the Span-Wagner equation of state through the CoolProp thermodynamic library and the Van der Waals equation of state, both in the ideal and non-ideal compressible fluid-dynamics regimes, by comparing it to the standard total energy update and analytical solutions where available.

翻译：本研究提出了一种通过以守恒方式显式更新通用热力学变量（如温度、压力或熵）而非总能量来求解欧拉方程的方法。所提出的方法适用于任意状态方程和空间离散格式。当使用复杂状态方程（如Span-Wagner方程）时，选择温度作为通用热力学变量可大幅降低热力学评估相关的计算成本。本文展示了采用先进热力学模型的计算结果，并分析了计算时间。研究特别关注总能量守恒、激波传播速度及跳跃条件。通过将本方法与标准总能量更新法及现有解析解进行对比，使用CoolProp热力学库中的Span-Wagner状态方程和范德瓦尔斯状态方程，在理想与非理想可压缩流体动力学体系下进行了全面测试。