Numerical Simulation of a Class of Nonlinear Wave Equations by Lattice Boltzmann Method  

作　　者：Yali Duan Linghua Kong Min Guo 

机构地区：[1]School of Mathematical sciences,University of Science and Technology of China,Hefei 230026.Anhui,People's Republic of China [2]School of Mathematics and Information Science,Jiangxi Normal University,Nanchang 330022,Jiangxi,People's Republic of China [3]Department of Basic,North China College of Mechanics and Electrics,Changzhi 046000,Shanxi,People's Republic of China

出　　处：《Communications in Mathematics and Statistics》2017年第1期13-35,共23页数学与统计通讯（英文）

基　　金：The authors are very thankful to the reviewers for their valuable suggestions toimprove the quality of the paper.This work is supported by National Natural Science Foundation of China(Nos.11101399,11271171,11301234);the Provincial Natural Science Foundation of Jiangxi(Nos.20161ACB20006,20142BCB23009,20151BAB201012).

摘　　要：In this paper,we develop a lattice Boltzmann model for a class ofone-dimensional nonlinear wave equations,including the second-order hyperbolictelegraph equation,the nonlinear Klein-Gordon equation,the damped and undampedsine-Gordon equation and double sine-Gordon equation.By choosing properly theconservation condition between the macroscopic quantity u,and the distributionfunctions and applying the Chapman-Enskog expansion,the governing equation isrecovered correctly from the lattice Boltzmann equation.Moreover,the local equilib-rium distribution function is obtained.The results of numerical examples have beencompared with the analytical solutions to confirm the good accuracy and the applica-bility of our scheme.

关 键 词：Lattice Boltzmann method Second-order hyperbolic telegraph equation Klein-Gordon equation Sine-Gordon equation Chapman-Enskog expansion 

分 类 号：O17[理学—数学]