可压缩流体流动的热力学效应与高分辨率方法
Thermodynamical Effects and High Resolution Methods for Compressible Fluid Flows
AI总结：
本文探讨了可压缩流体流动中热力学效应在高分辨率方法设计中的作用，通过改进GRP求解器展示了热力学变化如何影响强波的数值解，同时证明了该求解器适用于通用状态方程。
摘要：
可压缩流体流动与不可压缩流体流动的根本区别在于热力学的参与。这一差异应在数值方法的设计中体现出来，而熵不等式作为概念导数，用于反映不可逆过程并被某些一阶方案验证。本文通过改进GRP求解器，展示了热力学变化如何整合到可压缩流体流动的高分辨率方法设计中，并通过数值实验证明了热力学效应在强波求解中的重要性。作为副产品，本文还表明GRP求解器适用于通用状态方程，并且不依赖于技术论据。
英文摘要：
One of the fundamental differences of compressible fluid flows from incompressible fluid flows is the involvement of thermodynamics. This difference should be manifested in the design of numerical methods and seems often be neglected in addition that the entropy inequality, as a conceptual derivative, is taken into account to reflect irreversible processes and verified for some first order schemes. In this paper, we refine the GRP solver to illustrate how the thermodynamical variation is integrated into the design of high resolution methods for compressible fluid flows and demonstrate numerically the importance of thermodynamic effect in the resolution of strong waves. As a by-product, we show that the GRP solver works for generic equations of state, and is independent of technical arguments.
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