Cole-Hopf Transformation Based Lattice Boltzmann Model for One-dimensional Burgers' Equation

被引：0
|
作者：
亓晓同 [1 ,2 ]
施保昌 [1 ,2 ]
柴振华 [1 ,2 ]
机构：
[1] School of Mathematics and Statistics,Huazhong University of Science and Technology
[2] Hubei Key Laboratory of Engineering Modeling and Scientific Computing,Huazhong University of Science and Technology
来源：
Communications in Theoretical Physics | 2018年 / 69卷 / 03期
基金：
中国国家自然科学基金;
关键词：
Burgers; equation; Cole-Hopf transformation; lattice Boltzmann model;
D O I：
暂无
中图分类号：
O175.2 [偏微分方程];
学科分类号：
070104 ;
摘要：
In this paper,we present a Cole-Hopf transformation based lattice Boltzmann(LB) model for solving one-dimensional Burgers’ equation,and compared to available LB models,the effect of nonlinear convection term can be eliminated.Through Chapman-Enskog analysis,it can be found that the converted diffusion equation based on the Cole-Hopf transformation can be recovered correctly from present LB model.Some numerical tests are also performed to validate the present LB model,and the numerical results show that,similar to previous LB models,the present model also has a second-order convergence rate in space,but it is more accurate than the previous ones.
引用
收藏
页码：329 / 335
页数：7
相关论文
共 50 条
  • [1] Cole-Hopf Transformation Based Lattice Boltzmann Model for One-dimensional Burgers' Equation
    Qi, Xiao-Tong
    Shi, Bao-Chang
    Chai, Zhen-Hua
    COMMUNICATIONS IN THEORETICAL PHYSICS, 2018, 69 (03) : 329 - 335
  • [2] A lattice Boltzmann model based on Cole-Hopf transformation for N-dimensional coupled Burgers' equations
    Rong, Fumei
    Li, Qianhuan
    Shi, Baochang
    Chai, Zhenhua
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2023, 134 : 101 - 111
  • [3] COLE-HOPF TRANSFORMATION AS NUMERICAL TOOL FOR THE BURGERS EQUATION
    Ohwada, Taku
    APPLIED AND COMPUTATIONAL MATHEMATICS, 2009, 8 (01) : 107 - 113
  • [4] A generalized Cole-Hopf transformation for a two-dimensional burgers equation with a variable coefficient
    B. Mayil Vaganan
    M. Senthilkumaran
    T. Shanmuga Priya
    Indian Journal of Pure and Applied Mathematics, 2012, 43 : 591 - 600
  • [5] A GENERALIZED COLE-HOPF TRANSFORMATION FOR A TWO-DIMENSIONAL BURGERS EQUATION WITH A VARIABLE COEFFICIENT
    Vaganan, B. Mayil
    Senthilkumaran, M.
    Priya, T. Shanmuga
    INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 2012, 43 (06): : 591 - 600
  • [6] A Cole-Hopf Transformation Based Fourth-Order Multiple-Relaxation-Time Lattice Boltzmann Model for the Coupled Burgers' Equations
    Chen, Ying
    Liu, Xi
    Chai, Zhenhua
    Shi, Baochang
    JOURNAL OF SCIENTIFIC COMPUTING, 2025, 103 (01)
  • [7] An implicit tailored finite point method for the Burgers' equation: leveraging the Cole-Hopf transformation
    Shyaman, V. P.
    Sreelakshmi, A.
    Awasthi, Ashish
    PHYSICA SCRIPTA, 2024, 99 (07)
  • [8] The generalized Cole-Hopf transformation to a general variable coefficient Burgers equation with linear damping term
    Wang, Mingliang
    Zhang, Jinliang
    Li, Erqiang
    Xin, Xiaofei
    APPLIED MATHEMATICS LETTERS, 2020, 105
  • [9] The generalized Cole-Hopf transformation for a generalized Burgers-Fisher equation with spatiotemporal variable coefficients
    Shang, Yadong
    Chen, Quting
    APPLIED MATHEMATICS LETTERS, 2021, 117
  • [10] Stochastic Burgers PDEs with random coefficients and a generalization of the Cole-Hopf transformation
    Englezos, Nikolaos
    Frangos, Nikolaos E.
    Kartala, Xanthi-Isidora
    Yannacopoulos, Athanasios N.
    STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2013, 123 (08) : 3239 - 3272
12345