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Lattice Boltzmann method for one and two-dimensional Burgers equation

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  • Zhang, Jianying
  • Yan, Guangwu

Abstract

In this paper, a new method, higher-order moment lattice Boltzmann method for one and two-dimensional Burgers’ equation is proposed. The lattice Boltzmann models presented here are based on a series of lattice Boltzmann equations in different time scales. In order to achieve higher order accuracy, we use seven and four moments of the equilibrium distribution function in one and two-dimensional models respectively. We find two kinds of strategy to seek equilibrium distribution functions for the two-dimensional model with second order accuracy. These two are equivalent when a scale factor k=23. Lastly, we provide a fine numerical result of a one-dimensional Burgers’ equation. Numerical examples show the method can be used to simulate one and two-dimensional Burgers’ equation.

Suggested Citation

  • Zhang, Jianying & Yan, Guangwu, 2008. "Lattice Boltzmann method for one and two-dimensional Burgers equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(19), pages 4771-4786.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:19:p:4771-4786
    DOI: 10.1016/j.physa.2008.04.002
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    References listed on IDEAS

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    1. Velivelli, A.C. & Bryden, K.M., 2006. "Parallel performance and accuracy of lattice Boltzmann and traditional finite difference methods for solving the unsteady two-dimensional Burger's equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 362(1), pages 139-145.
    2. Kudryashov, Nikolai A. & Demina, Maria V., 2007. "Polygons of differential equations for finding exact solutions," Chaos, Solitons & Fractals, Elsevier, vol. 33(5), pages 1480-1496.
    3. Horii, Zene, 2005. "Mass transport theory for the Toda lattices, dispersive and dissipative," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 350(2), pages 349-378.
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    Cited by:

    1. Liu, Fang & Shi, Weiping & Wu, Fangfang, 2016. "A lattice Boltzmann model for the generalized Boussinesq equation," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 331-342.
    2. Kim, Philsu & Kim, Dojin, 2020. "Convergence and stability of a BSLM for advection-diffusion models with Dirichlet boundary conditions," Applied Mathematics and Computation, Elsevier, vol. 366(C).
    3. Egidi, Nadaniela & Maponi, Pierluigi, 2016. "Artificial boundary conditions for the Burgers equation on the plane," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 1-14.
    4. Wang, Huimin, 2016. "A lattice Boltzmann model for the ion- and electron-acoustic solitary waves in beam-plasma system," Applied Mathematics and Computation, Elsevier, vol. 279(C), pages 62-75.

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