变系数广义KdV-Burgers方程的格子Boltzmann模型

Abstract

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

CLC Number:

O175

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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References 15

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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

[1]	YANG Ai-Li, WU Yu-Jiang, SONG Lun-Ji. A Class of Generalized Three Dimensional Convection-Diffusion Equations with Multi-Level Incremental Unknowns Method [J]. Acta mathematica scientia,Series A, 2009, 29(3): 564-572.
[2]	Zhang Jinliang ; Wang Mingliang ; Wang Yueming. The Extended F-expansion Method and the Exact Solutions to the KdV and mKdV Equation with Variable Coefficients [J]. Acta mathematica scientia,Series A, 2006, 26(3): 353-360.

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

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