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A unified lattice Boltzmann model for some nonlinear partial differential equations

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  • Chai, Zhenhua
  • Shi, Baochang
  • Zheng, Lin

Abstract

In this paper, a unified and novel lattice Boltzmann model is proposed for solving nonlinear partial differential equation that has the form DUt+αUUx+βUnUx−γUxx+δ Uxxx=F(x,t). Numerical results agree well with the analytical solutions and results derived by existing literature, which indicates the present model is satisfactory and efficient on solving nonlinear partial differential equations.

Suggested Citation

  • Chai, Zhenhua & Shi, Baochang & Zheng, Lin, 2008. "A unified lattice Boltzmann model for some nonlinear partial differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 36(4), pages 874-882.
    • Handle: RePEc:eee:chsofr:v:36:y:2008:i:4:p:874-882
    DOI: 10.1016/j.chaos.2006.07.023
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    References listed on IDEAS

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    1. Helal, M.A. & Mehanna, M.S., 2006. "A comparison between two different methods for solving KdV–Burgers equation," Chaos, Solitons & Fractals, Elsevier, vol. 28(2), pages 320-326.
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    Cited by:

    1. Lai, Huilin & Ma, Changfeng, 2014. "A new lattice Boltzmann model for solving the coupled viscous Burgers’ equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 395(C), pages 445-457.
    2. Krivovichev, Gerasim V., 2018. "Linear Bhatnagar–Gross–Krook equations for simulation of linear diffusion equation by lattice Boltzmann method," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 102-119.
    3. Li, Qianhuan & Chai, Zhenhua & Shi, Baochang, 2015. "A novel lattice Boltzmann model for the coupled viscous Burgers’ equations," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 948-957.

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