变系数广义KdV-Burgers方程的格子Boltzmann模型

数学物理学报 ›› 2021, Vol. 41 ›› Issue (5): 1283-1295.

变系数广义KdV-Burgers方程的格子Boltzmann模型

张宗宁(),李春光*(),董建强

^{北方民族大学数学与信息科学学院银川 750021}

收稿日期:2020-11-29 出版日期:2021-10-26 发布日期:2021-10-08
通讯作者: 李春光 E-mail:zzn5238@163.com;cglizd@hotmail.com
作者简介:张宗宁, E-mail: zzn5238@163.com
基金资助:
国家自然科学基金(11761005);宁夏高等教育一流学科建设资助项目(NXYLXK2017B09);北方民族大学研究生创新项目(YCX21156);北方民族大学校级一般项目(2020XYZSX02)

General Propagation Lattice Boltzmann Model for a Variable-Coefficient Compound KdV-Burgers Equation

Zongning Zhang(),Chunguang Li*(),jianqiang Dong

^{School of Mathematics and Information Science, North Minzu University, Yinchuan 750021}

Received:2020-11-29 Online:2021-10-26 Published:2021-10-08
Contact: Chunguang Li E-mail:zzn5238@163.com;cglizd@hotmail.com
Supported by:
the NSFC(11761005);the First-Class Disciplines Foundation of Ningxia(NXYLXK2017B09);the Postgraduate Innovation Project of North Minzu University(YCX21156);the University-level Scientific Research Projects of North Minzu University(2020XYZSX02)

摘要/Abstract

摘要：

该文研究了一类变系数广义KdV-Burgers方程的数值计算方法.首先，通过选择平衡态分布函数和加入修正函数，得到了一个具有变系数的广义KdV-Burgers方程的格子Boltzmann模型.该模型可以在没有任何假设的情况下准确地恢复出KdV-Burgers方程.其次，研究了方程中的非线性高阶导数项变化时的时空变化趋势，并与其解析解做对比，给出误差分析.最后，对方程的空间和时间做精度分析，根据仿真实验结果，模型可以达到2阶精度.数值结果表明，格子Boltzmann算法是一种令人满意的高效算法.

关键词: 格子Boltzmann方程, Chapman-Enskog分析, KdV-Burgers equation, 变系数

Abstract:

This paper studies the numerical calculation method of a kind of general Kdv-Burgers equation with variable coefficients. Firstly, a lattice Boltzmann model of the generalized KdV-Burgers equation with variable coefficients is obtained by selecting the equilibrium distribution function and adding the correction function. The model could accurately recover the KdV-Burgers equation without any assumptions. Secondly, this paper studies the temporal and spatial change trend of the nonlinear high-order derivative term in the equation, and compares it with the analytical solution, and then gives an error analysis. Finally, This paper analyzes the precision of the space and time of the equation. According to the simulation experiment results, the model could reach 2nd order accuracy. Numerical results show that the current lattice Boltzmann model is a satisfactory and efficient algorithm.

Key words: Lattice Boltzmann equation, Chapman-Enskog analysis, KdV-Burgers equation, Variable coefficient

中图分类号:

O175

张宗宁,李春光,董建强. 变系数广义KdV-Burgers方程的格子Boltzmann模型[J]. 数学物理学报, 2021, 41(5): 1283-1295.

Zongning Zhang,Chunguang Li,jianqiang Dong. General Propagation Lattice Boltzmann Model for a Variable-Coefficient Compound KdV-Burgers Equation[J]. Acta mathematica scientia,Series A, 2021, 41(5): 1283-1295.

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Parameters	t=0.5	t=1.0	t=1.5	t=2.0
E₂	5.1836e-04	4.9568e-04	6.1178e-04	7.6003e-04
E_∞	0.0364	0.0349	0.0478	0.0585
GRE	0.0334	0.0303	0.0369	0.0429

Parameters	t=1.0	t=2.0	t=3.0
E₂	1.0660e-04	7.9380e-05	7.0678e-05
E_∞	0.0230	0.0151	0.0125
GRE	0.0343	0.0267	0.0252

Parameters	t=1.0	t=2.0	t=3.0
E₂	2.2805e-04	2.8858e-04	2.2420e-04
E_∞	0.0043	0.0055	0.0043
GRE	0.0593	0.0750	0.0583

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