留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

一类含源Boussinesq系统解的数值分析及仿真

何郁波 董晓亮 林晓艳

何郁波, 董晓亮, 林晓艳. 一类含源Boussinesq系统解的数值分析及仿真[J]. 应用数学和力学, 2018, 39(8): 961-978. doi: 10.21656/1000-0887.380126
引用本文: 何郁波, 董晓亮, 林晓艳. 一类含源Boussinesq系统解的数值分析及仿真[J]. 应用数学和力学, 2018, 39(8): 961-978. doi: 10.21656/1000-0887.380126
HE Yubo, DONG Xiaoliang, LIN Xiaoyan. Numerical Analysis and Simulation of Solutions to a Class of Boussinesq Systems With Source Terms[J]. Applied Mathematics and Mechanics, 2018, 39(8): 961-978. doi: 10.21656/1000-0887.380126
Citation: HE Yubo, DONG Xiaoliang, LIN Xiaoyan. Numerical Analysis and Simulation of Solutions to a Class of Boussinesq Systems With Source Terms[J]. Applied Mathematics and Mechanics, 2018, 39(8): 961-978. doi: 10.21656/1000-0887.380126

一类含源Boussinesq系统解的数值分析及仿真

doi: 10.21656/1000-0887.380126
基金项目: 国家自然科学基金(11471137;11501232;11601012);宁夏自然科学基金(NZ17103)
详细信息
    作者简介:

    何郁波(1979—),男,副教授,博士(通讯作者. E-mail: heyinprc@csu.edu.cn);董晓亮(1981—),男,副教授,博士(E-mail: dongxl@stu.xidian.edu.cn).

  • 中图分类号: TP301.6;O241.82

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

Funds: The National Natural Science Foundation of China(11471137;11501232;11601012)
  • 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Chapman-Enskog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.
  • [1] 熊志强. Boussinesq方程模型的数值造波方法研究[D]. 硕士学位论文. 天津: 天津大学, 2007.(XIONG Zhiqiang. Numerical wave generation in Boussinesq equation models[D]. Master Thesis. Tianjin: Tianjin University, 2007.(in Chinese))
    [2] 王颖. 几类Boussinesq方程的Cauchy问题[D]. 博士学位论文. 成都: 四川大学, 2007.(WANG Ying. The Cauchy problems for some classes of Boussinesq equations[D]. PhD Thesis. Chengdu: Sichuan University, 2007.(in Chinese))
    [3] MILES J W. Solitary waves[J]. Annual Review of Fluid Mechanics,1980,12: 11-43.
    [4] MILEWSKI P A, KELLER J B. Three-dimensional water waves[J]. Studies in Applied Mathematics, 1996,97(2): 149-166.
    [5] TSUTSUMI M, MATAHASHI T. On the Cauchy problem for the Boussinesq type equation[J]. Mathematics Japonica,1991,36: 371-379.
    [6] BONA J, SACHS R. Global existence of smooth solution and stabilityof solitary waves for a generalized Boussinesq equation[J]. Communications in Mathematical Physics,1988,118(1): 12-29.
    [7] KALANTAROV V K, LADYZHENSKAYA O A. The occurrence of collapse for quasilinear equations of parabolic and hyperbolic types[J]. Journal of Mathematical Sciences,1978,10(1): 53-70.
    [8] LEVIN H A, SLEEMAN B D. A note on the nonexistence of global solutions of initial-boundary value problems for the Boussinesq equation utt=3uxxx+uxx-12(u2)xx[J].Journal of Mathematical Analysis and Applications,1985,107(1): 206-210.
    [9] HIROTA R. Exact N-solition solutions of the wave equation of long waves in shallow-water and in nonlinear lattices[J]. Journal of Mathematical Physics,1973,14(7): 810-814.
    [10] CLARKSON P. New exact solution of the Boussinesq equation[J]. European Journal of Applied Mathematics,1990,1(3): 279-300.
    [11] PEREGRINE D H. Long waves on a beach[J]. Journal of Fluid Mechanics,1967,27(4): 815-827.
    [12] WEI G, KIRBY J T, GRILLI S T, et al. A fully nonlinear Boussinesq model for surface wave: part I, highly nonlinear unsteady waves[J]. Journal of Fluid Mechanics,1995,294: 71-92.
    [13] 李春颖. 基于Boussinesq方程的海岸地区波浪数学模型研究[D]. 硕士学位论文. 天津: 天津大学, 2003.(LI Chunying. Research on numerical model for waves in coastal region based on Boussinesq equations[D]. Master Thesis. Tianjin: Tianjin University, 2003.(in Chinese))
    [14] 王涛. 高阶Boussinesq方程的数值模型[D]. 硕士学位论文. 大连: 大连理工大学, 2002.(WANG Tao. The numerical model of the high order Boussinesq equation[D]. Master Thesis. Dalian: Dalian University of Technology, 2002.(in Chinese))
    [15] OLLILA S, DENNISTON C, KARTTUNEN M, et al. Fluctuating Lattice-Boltzmann model for complex fluids[J]. Journal of Chemical Physics,2011,134(6): 549-197.
    [16] FALLAH K, KHAYAT M, BORGHEI M H, et al. Multiple-relaxation-time lattice Boltzmann simulation of non-Newtonian flows past a rotating circular cylinder[J].Journal of Non-Newtonian Fluid Mechanics,2012,177/178: 1-14.
    [17] MAO W, GUO Z L, WANG L. Lattice Boltzmann simulation of the sedimentation of particles with thermal convection[J]. Acta Physica Sinica,2013,62(8): 786-790.
    [18] YANG T Z, JI S, YANG X D, et al. Microfluid-induced nonlinear free vibration of microtubes[J]. International Journal of Engineering Science,2014,76(4): 47-55.
    [19] HE Y B, TANG X H, LIN X Y. Numerical simulation of a class of Fitz Hugh-Nagumo systems based on the lattice Boltzmann method[J].Acta Physica Sinica,2016,65(15): 133-142.
    [20] VARLAMOV V V. Long-time asymptotics of solutions of the second initial-boundary value problem for the damped Boussinesq equation[J]. Abstract and Applied Analysis,1998,2(3/4): 281-289.
    [21] 赖惠林. 几类非线性波方程的格子玻尔兹曼模型的数值分析及模拟[D]. 博士学位论文. 福州: 福建师范大学, 2012.(LAI Huilin. Numerical analysis and simulation of lattice Boltzmann models for some nonlinear wave equations[D]. PhD Thesis. Fuzhou: Fujian Normal University, 2012.(in Chinese))
    [22] MAKHANKOV V G. Dynamics of classical solitons(in non-integrable systems)[J]. Physics Reports,1978,35(1): 1-128.
    [23] CLARKSON P A, KRUSKAL M D. New similarity reductions of the Boussinesq equation[J]. Journal of Mathematical Physics,1989,30(10): 2201-2213.
    [24] DEIFT P, TOMEI C, TRUBOWITZ E. Inverse settering and the Boussinesq equation[J]. Pure and Applied Mathematics,1982,35(5): 567-628.
    [25] SHU C W, OSHER S. Efficient implementation of essentially non-oscillatory shock-capturing schemes[J]. Journal of Computational Physics,1998,77(2): 439-471.
    [26] GUO Z L, ZHENG C G, SHI B C. Non-equilibrium extrapolation method for velocity and pressure boundary conditions in the lattice Boltzmann method[J]. Chinese Physics,2002,11(4): 366-374.
    [27] FU Z T, LIU S K, LIU S D, et al. The JEFE method and periodic solutions of two kinds of nonlinear wave equations[J]. Communications in Nonlinear Science and Numerical Simulation,2003,8(2): 67-75.
  • 加载中
计量
  • 文章访问数:  577
  • HTML全文浏览量:  65
  • PDF下载量:  709
  • 被引次数: 0
出版历程
  • 收稿日期:  2017-06-08
  • 修回日期:  2017-11-07
  • 刊出日期:  2018-08-15

目录

    /

    返回文章
    返回