We propose two novel two-state approximate Riemann solvers for the compressible Euler equations which are provably entropy dissipative and suitable for the simulation of low Mach numbers. What is new, is that one of our two methods in addition is provably kinetic energy stable. Both methods are based on the entropy satisfying and kinetic energy consistent methods of Chandrashekar (2013). The low Mach number compliance is achieved by rescaling some speed of sound terms in the diffusion matrix in the spirit of Li & Gu (2008). In numerical tests we demonstrate the low Mach number compliance and the entropy stability of the proposed fluxes.

中文翻译：

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适用于所有马赫数的可压缩欧拉方程的熵稳定数值通量

我们为可压缩的欧拉方程提出了两种新颖的两态近似黎曼求解器，这些方程可证明是熵耗散的，适用于低马赫数的模拟。新的是，我们的两种方法之一是可证明动能稳定的。这两种方法都基于 Chandrashekar (2013) 的熵满足和动能一致方法。本着 Li & Gu (2008) 的精神，通过重新调整扩散矩阵中的某些声速项来实现低马赫数顺应性。在数值测试中，我们证明了所提出的通量的低马赫数符合性和熵稳定性。