Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (5): 1283-1295.

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

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

  1. 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;
  • 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)


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