Zakharov-Rubenchik方程组的格子Boltzmann方法  

Lattice Boltzmann method for the Zakharov-Rubenchik equations

作　　者：宋艺[1] 戴厚平[2] SONG Yi;DAI Houping(Academic Affairs Office,Changsha Social Work College,Changsha,Hunan 414004,China;School of Mathematics and Statistics,Jishou University,Jishou,Hunan 416000,China)

机构地区：[1]长沙民政职业技术学院教务处,长沙410004 [2]吉首大学数学与统计学院,湖南吉首416000

出　　处：《湖南城市学院学报（自然科学版）》2024年第4期73-78,共6页Journal of Hunan City University:Natural Science

基　　金：湖南省教育科学“十四五”规划课题(XJK22BZY008)。

摘　　要：Zakharov-Rubenchik方程组常用于描述非线性介质中高、低频波间相互作用的波耦合现象。本文针对该方程组的数值求解问题,构建了一种格子Boltzmann方法的D1Q3演化模型,并利用Chapman-Enskog展开和多尺度分析技术,推导出了各个方向的平衡态分布函数和修正函数的具体表达式,从而将所建的演化模型准确恢复到宏观方程组。最后,通过数值算例证明了该方法的有效性。Zakharov-Rubenchik equationsare often used to describe the wave coupling phenomenon of interaction between high and low frequency waves in nonlinear media.In this paper,a D1Q3 evolution model of lattice Boltzmann method is constructed for the numerical solution of the equations.By using Chapman-Enskog expansion and multi-scale analysis technology,the specific expressions of equilibrium distribution function and correction function in all directions are derived,so that the established evolution model can be accurately restored to the macroscopic equations.Finally,numerical example results demonstrate the effectiveness of the method.

关 键 词：一维Zakharov-Rubenchik方程组 格子BOLTZMANN方法 数值求解 非线性偏微分方程 

分 类 号：O242.1[理学—计算数学]