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.

引用

页码：473 / 482

页数：10