论文标题
在可压缩流模拟中对能量方程的数值处理
Numerical treatment of the energy equation in compressible flows simulations
论文作者
论文摘要
我们分析了无需电击流的可压缩欧拉方程系统的各种离散化的保护特性，特别关注能量方程的处理以及其他热力学量的诱导离散方程。该分析在理论上和数字上都进行，并考虑了表征各种配方的两个重要因素，即能量方程的选择以及用于对流术语的离散化的分裂。分析的能量方程是总能量和内部能量，总焓，压力，声音和熵的速度。在所有情况下，检查对流术语的离散化都是由局部保守和动能保存方案制成的。突出显示了各种配方之间的一些重要关系，并且通过考虑两个广泛使用的测试用例来评估各种方案的性能。以及文献中一些流行的配方，还分析了新的且潜在的有用的配方。
We analyze the conservation properties of various discretizations of the system of compressible Euler equations for shock-free flows, with special focus on the treatment of the energy equation and on the induced discrete equations for other thermodynamic quantities. The analysis is conducted both theoretically and numerically and considers two important factors characterizing the various formulations, namely the choice of the energy equation and the splitting used in the discretization of the convective terms. The energy equations analyzed are total and internal energy, total enthalpy, pressure, speed of sound and entropy. In all the cases examined the discretization of the convective terms is made with locally conservative and kinetic-energy preserving schemes. Some important relations between the various formulations are highlighted and the performances of the various schemes are assessed by considering two widely used test cases. Together with some popular formulations from the literature, also new and potentially useful ones are analyzed.
