关于可压缩Euler方程Harten单参数熵族中一个成员守恒的数值通量的注记
A Note on Numerical Fluxes Conserving a Member of Harten's One-Parameter Family of Entropies for the Compressible Euler Equations
摘要：
熵守恒的数值通量是现代高阶熵耗散守恒律离散的基石。除了熵守恒之外，模拟连续水平的其他结构性质，如压力平衡和动能守恒也很重要。本文证明了对于既保持压力平衡又具有与压力无关的密度通量的可压缩Euler方程，不存在守恒Harten熵的数值通量。这与基于物理熵的通量形成对比，在物理熵的通量中，甚至可以另外实现动能守恒。
英文摘要：
Entropy-conserving numerical fluxes are a cornerstone of modern high-order entropy-dissipative discretizations of conservation laws. In addition to entropy conservation, other structural properties mimicking the continuous level such as pressure equilibrium and kinetic energy preservation are important. This note proves that there are no numerical fluxes conserving (one of) Harten's entropies for the compressible Euler equations that also preserve pressure equilibria and have a density flux independent of the pressure. This is in contrast to fluxes based on the physical entropy, where even kinetic energy preservation can be achieved in addition.
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