This study proposes a novel spatial discretization procedure for the compressible Euler equations which guarantees entropy conservation at a discrete level when an arbitrary equation of state is assumed. The proposed method, based on a locally-conservative discretization, guarantees also the spatial conservation of mass, momentum, and total energy and is kinetic energy-preserving. In order to achieve the entropy-conservation property for an arbitrary non-ideal gas, a general strategy is adopted based on the manipulation of discrete balance equations through the imposition of global entropy conservation and the use of a summation by parts rule. The procedure, which is extended to an arbitrary order of accuracy, conducts to a general form of the internal-energy numerical flux which results in a nonlinear function of thermodynamic and dynamic variables and still admits the mass flux as a residual degree of freedom. The effectiveness of the novel entropy-conservative formulation is demonstrated through numerical tests making use of some of the most popular cubic equations of state.

翻译：本研究提出了一种新颖的空间离散化方法，用于可压缩欧拉方程，该方法在假设任意状态方程时，能够在离散层面上保证熵守恒。所提出的方法基于局部守恒离散化，同时保证了质量、动量和总能量的空间守恒，并且是动能守恒的。为了实现任意非理想气体的熵守恒特性，采用了一种通用策略，该策略基于通过施加全局熵守恒和使用分部求和规则来操作离散平衡方程。该过程可扩展至任意精度阶数，导出了内能数值通量的一般形式，该形式是热力学和动力学变量的非线性函数，并且仍将质量通量作为剩余自由度。通过使用一些最流行的立方型状态方程进行数值测试，验证了这种新颖的熵守恒格式的有效性。