Second-order Boltzmann schemes for compressible Euler equations in one and two space dimensions
Second-order Boltzmann schemes for compressible Euler equations in one and two space dimensions
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DOI：
10.1137/0729001
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发表时间：
1992-02
影响因子：
2.9
通讯作者：
B. Perthame
中科院分区：
文献类型：
--
作者：
B. Perthame
描述了一类求解可压缩Euler方程的二阶数值格式，并讨论了其L^1 $稳定性（即，$\rho \geqq 0$，$T \geqq 0$）。按照货车莱尔的方法，解决方案（$\rho $，u，$\sqrt T $在这里）表示为分段线性函数。坡度限制的必要性在方案的推导中自然出现，但它可以比通常使用的坡度重建更不严格。这些格式是用显式通量分裂公式写成的，在空间上自然是多维的;上绕是通过一个非常一般化的特征概念得到的：动力学特征。
A class of second-order numerical schemes for the compressible Euler equations is described, and their $L^1 $ stability (i.e., $\rho \geqq 0$, $T \geqq 0$) is proved. Following Van Leer’s approach, the solution ($\rho $, u,$\sqrt T $ here) is represented as piecewise linear functions. The necessity of a slope limitation appears naturally in the derivation of the schemes, but it can be less strict than the slope reconstructions usually used. These schemes are written in terms of explicit flux splitting formula and are naturally multidimensional in space; the upwinding is obtained through a very generalized notion of characteristics: the kinetic one.