This paper introduces a family of entropy-conserving finite-difference discretizations for the compressible flow equations. In addition to conserving the primary quantities of mass, momentum, and total energy, the methods also preserve kinetic energy and pressure equilibrium. The schemes are based on finite-difference (FD) representations of the logarithmic mean, establishing and leveraging a broader link between linear and nonlinear two-point averages and FD forms. The schemes are locally conservative due to the summation-by-parts property and therefore admit a local flux form, making them applicable also in finite-volume and finite-element settings. The effectiveness of these schemes is validated through various test cases (1D Sod shock tube, 1D density wave, 2D isentropic vortex, 3D Taylor Green vortex) that demonstrate exact conservation of entropy along with conservation of the primary quantities and preservation of pressure equilibrium.

翻译：本文提出了一类用于可压缩流动方程的熵守恒有限差分离散格式。这些方法不仅守恒质量、动量和总能量等基本物理量，还能保持动能和压力平衡。该格式基于对数平均的有限差分表示，建立并利用了线性与非线性两点平均与有限差分形式之间更广泛的联系。由于具有分部求和特性，这些格式具有局部守恒性，因此可采用局部通量形式，使其同样适用于有限体积和有限元框架。通过多种测试案例（一维Sod激波管、一维密度波、二维等熵涡、三维Taylor-Green涡）验证了这些格式的有效性，结果表明在守恒基本物理量和保持压力平衡的同时，实现了熵的精确守恒。