How to obtain higher-order multivariate Hermite expansion of Maxwell-Boltzmann distribution by using Taylor expansion?

被引：9
|
作者：
Shim, Jae Wan [1 ,2 ]
Gatignol, Renee [3 ,4 ]
机构：
[1] KIST, Seoul 136791, South Korea
[2] Univ Sci & Technol, Seoul 136791, South Korea
[3] Univ Paris 06, Inst Jean Rond dAlembert, F-75252 Paris 05, France
[4] CNRS, F-75252 Paris 05, France
来源：
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK | 2013年 / 64卷 / 03期
基金：
新加坡国家研究基金会;
关键词：
Series expansion; Hermite polynomials; Hermite series expansion; Taylor series expansion; Boltzmann equation;
D O I：
10.1007/s00033-012-0265-1
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We obtain the higher-order multivariate Hermite expansion of the Maxwell-Boltzmann distribution by using a new, compact tensorial notation and present a method to obtain the nth order multivariate Taylor expansion, which is identical to the nth order multivariate Hermite expansion of the Maxwell-Boltzmann distribution. This study enables us to find higher-order models of discrete kinetic theories such as the lattice Boltzmann theory.
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页码：473 / 482
页数：10
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