一类Equal Width波方程的介观数值模拟研究  

Mesoscopic Numerical Study of the Equal Width Wave Equations

作　　者：李德梅 赖惠林 甘延标[2] 林传栋 LI De-mei;LAI Hui-lin;GAN Yan-biao;LIN Chuan-dong(College of Mathematics and lnformatics,FJKLMAA,Fujian Normal University,Fuzhou 350117,China;Department of Basic Science,North China Institute of Aerospace Engineering,Lanffang 065000,China;Center for Combustion Energy,Department of Energy and Power Engineering,Tsinghua University,Beijing 100084,China)

机构地区：[1]福建师范大学数学与信息学院,福建省分析数学及应用重点实验室,福建福州350117 [2]北华航天工业学院基础科学部,河北廊坊065000 [3]清华大学能源与动力工程系,燃烧能源中心,北京100084

出　　处：《福建师范大学学报（自然科学版）》2018年第5期6-11,共6页Journal of Fujian Normal University：Natural Science Edition

基　　金：福建省自然科学基金资助项目(2018J01654); 河北省自然科学基金资助项目(A2017409014); 河北省教育厅重点项目(ZD2017001); 河北省人才工程培养经费资助科研项目(A201500111); 中国博士后科学基金(2017M620757)

摘　　要：针对Equal Width波方程的初边值问题,构造了一类非标准格子玻尔兹曼介观数值模型.通过Taylor展开和Chapman-Enskog多尺度分析,可以从该模型正确恢复出Equal Width波方程.同时,获得了相应的局部平衡态分布函数的具体表达式.通过选取带有解析解的初边值问题进行数值模拟,数值结果显示数值解与解析解十分吻合,表明所构造的格子玻尔兹曼介观数值模型在一定范围内是可行有效的.该模型能够为今后数值求解更复杂的偏微分方程提供借鉴经验.This paper considers the initial-boundary value problem of the Equal wave equation,and construct a non-standard lattice Boltzmann mesoscopic numerical model with an amending item. Through Taylor expansion and Chapman Enskog multi-scale analysis,the Equal Width wave equation can be recovered from the non-standard lattice Boltzmann equation. At the same time,the local equilibrium distribution function can be obtained. The initial boundary value problem with analytic solution is selected for numerical simulation,then we find the numerical solution agrees well with the analytical solution. Numerical results show that the lattice Boltzmann mesoscopic numerical model is feasible and effective in a certain range. This model can provide reference experience for solving more complicated partial differential equations.

关 键 词：Equal Width波方程 格子玻尔兹曼方法 Chapman-Enskog多尺度分析 

分 类 号：O242.1[理学—计算数学]