一类含源Boussinesq系统解的数值分析及仿真  

Numerical Analysis and Simulation of Solutions to a Class of Boussinesq Systems With Source Terms

作　　者：何郁波 董晓亮 林晓艳 HE Yubo;DONG Xiaoliang;LIN Xiaoyan(School of Mathematics and Computation Science,Huaihua University,Huaihua,Hunan 418008,P.R.China;School of Mathematics and Information Science,North Minzu University Yinchuan 750021,P.R.China)

机构地区：[1]怀化学院数学与计算科学学院,湖南怀化418008 [2]北方民族大学数学与信息科学学院,银川750021

出　　处：《应用数学和力学》2018年第8期961-978,共18页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11471137;11501232;11601012);宁夏自然科学基金(NZ17103)~~

摘　　要：对于一类含源的高阶非线性波动方程Boussinesq方程的初边值问题,利用D1Q5模型的格子Boltzmann方程,通过选取不同的演化方程和局部平衡态分布函数及修正函数,应用ChapmanEnskog多尺度技术和Taylor展开技术,提出了具有五阶高精度带修正函数的非标准格子Boltzmann模型.应用所提出的模型,仿真模拟了几个具有精确解的Boussinesq方程初边值系统,并与传统的修正有限差分法(MFDM)进行了对比,结果表明该文模型所得的数值解与精确解吻合,其模误差小于MFDM.此外,还针对精确解未知的Boussinesq方程初边值系统进行了数值仿真,并与MFDM进行了对比.数值结果表明,两种计算格式的数值解比较吻合,进一步证明了文中所构造模型的有效性和稳定性.For a class of initial value problems of the high-order Boussinesq systems with source terms,a D1 Q5 nonstandard lattice Boltzmann model（ LBM） with correction functions and source terms was proposed. Different local equilibrium distribution functions and correction functions were selected,and the nonlinear wave equation was recovered by means of the Chapman-Enskog multi-scale analysis and the Taylor expansion technique. Some initial boundary value problems of the Boussinesq systems with analytical solutions were simulated to verify the effectiveness of the LBM. The results show that the numerical solutions agree well with the analytical solutions and the norm errors obtained with the LBM are smaller than those with the modified finite difference method（ MFDM）. Furthermore,some problems without analytical solutions were numerically studied with the present method and the MFDM. The comparison shows that the numerical solutions from the LBM are in good agreement with those from the MFDM,which validates the effectiveness and stability of the proposed model.

关 键 词：格子BOLTZMANN模型 BOUSSINESQ方程 Chapman-Enskog展开 修正有限差分法 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构] O241.82[自动化与计算机技术—计算机科学与技术]