非线性耦合长短波方程的格子Boltzmann模型求解

doi:10.13438/j.cnki.jdzk.2022.03.002

吉首大学学报（自然科学版） ›› 2022, Vol. 43 ›› Issue (3): 7-14.DOI: 10.13438/j.cnki.jdzk.2022.03.002

非线性耦合长短波方程的格子Boltzmann模型求解

宋通政，戴厚平，冯舒婷，魏雪丹

(吉首大学数学与统计学院，湖南吉首 416000)

出版日期:2022-05-25 发布日期:2022-09-06
通讯作者: 戴厚平(1979—)，男，湖南邵阳人，吉首大学数学与统计学院副教授，主要从事微分方程数值解研究.
作者简介:宋通政(1997—)，男，山东潍坊人，吉首大学数学与统计学院硕士研究生，主要从事微分方程数值解研究
基金资助:
湖南省自然科学基金资助项目(2021JJ30548);湖南省教育厅科学研究重点项目(21A0329);吉首大学校级科研项目(JDY21015)

Lattice Boltzmann Model for Solving Nonlinear Coupled Long and Short Wave Equations

SONG Tongzheng,DAI Houping,FENG Shuting,WEI Xuedan

(College of Mathematics and Statistics,Jishou University,Jishou 416000,Hunan China)

Online:2022-05-25 Published:2022-09-06

摘要/Abstract

摘要：通过Taylor展开和Chapman-Enskog多尺度展开技术推导出平衡态分布函数和修正函数，并将两函数引入具有双分布函数的D1Q3格子Boltzmann模型，并利用该模型求解了一类非线性耦合的长短波方程的初边值问题. 对于平面波解和孤立波解，数值模拟结果验证了该模型求解非线性耦合的长短波方程的初边值问题的有效性.

关键词： 长短波方程, 格子Boltzmann模型, Taylor展开, Chapman-Enskog多尺度展开

Abstract: With Taylor expansion and Chapman-Enskog multi-scale expansion techniques,the equilibrium distribution functions and the correction functions are derived,and the two functions are introduced into the D1Q3 lattice Boltzmann model with two distribution functions.With this model,the initial-boundary value problem for a class of nonlinear coupled long-short wave equations is solved.For the plane wave and solitary wave solutions,the numerical simulation results verify the validity of the model for solving the nonlinear coupled initial-boundary value problems of the long-short wave equation.

Key words: long and short wave equations, lattice Boltzmann model, Taylor expansion, Chapman-Enskog multi-scale expansion

宋通政, 戴厚平, 冯舒婷, 魏雪丹. 非线性耦合长短波方程的格子Boltzmann模型求解[J]. 吉首大学学报（自然科学版）, 2022, 43(3): 7-14.

SONG Tongzheng, DAI Houping, FENG Shuting, WEI Xuedan. Lattice Boltzmann Model for Solving Nonlinear Coupled Long and Short Wave Equations[J]. Journal of Jishou University(Natural Sciences Edition), 2022, 43(3): 7-14.

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非线性耦合长短波方程的格子Boltzmann模型求解

Lattice Boltzmann Model for Solving Nonlinear Coupled Long and Short Wave Equations

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