期刊
BIT NUMERICAL MATHEMATICS
卷 60, 期 3, 页码 791-824出版社
SPRINGER
DOI: 10.1007/s10543-019-00789-w
关键词
Isothermal Euler; Polytropic Euler; Entropy stability; Finite volume; Summation-by-parts; Nodal discontinuous Galerkin spectral element method
In this work we analyze the entropic properties of the Euler equations when the system is closed with the assumption of a polytropic gas. In this case, the pressure solely depends upon the density of the fluid and the energy equation is not necessary anymore as the mass conservation and momentum conservation then form a closed system. Further, the total energy acts as a convex mathematical entropy function for the polytropic Euler equations. The polytropic equation of state gives the pressure as a scaled power law of the density in terms of the adiabatic index gamma As such, there are important limiting cases contained within the polytropic model like the isothermal Euler equations (gamma=1 and the shallow water equations (gamma=2 We first mimic the continuous entropy analysis on the discrete level in a finite volume context to get special numerical flux functions. Next, these numerical fluxes are incorporated into a particular discontinuous Galerkin (DG) spectral element framework where derivatives are approximated with summation-by-parts operators. This guarantees a high-order accurate DG numerical approximation to the polytropic Euler equations that is also consistent to its auxiliary total energy behavior. Numerical examples are provided to verify the theoretical derivations, i.e., the entropic properties of the high order DG scheme.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据