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Lattice Boltzmann model for time sub-diffusion equation in Caputo sense

Author

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  • Du, Rui
  • Sun, Dongke
  • Shi, Baochang
  • Chai, Zhenhua

Abstract

Anomalous diffusions, including subdiffusion and superdiffusion, are usually encountered in many diverse applications in science and engineering. Although many numerical methods have been proposed to study anomalous diffusion problems that are modeled by fractional advection-diffusion equations, in this paper, a fresh lattice Boltzmann (LB) model for time sub-diffusion equation in Caputo sense is proposed. Through the Chapman-Enskog analysis, the time-fractional diffusion equation can be recovered from the developed LB model. In addition, we also test the present LB model through some problems, and find that the numerical results agree well with the analytical solutions to these problems.

Suggested Citation

  • Du, Rui & Sun, Dongke & Shi, Baochang & Chai, Zhenhua, 2019. "Lattice Boltzmann model for time sub-diffusion equation in Caputo sense," Applied Mathematics and Computation, Elsevier, vol. 358(C), pages 80-90.
    • Handle: RePEc:eee:apmaco:v:358:y:2019:i:c:p:80-90
    DOI: 10.1016/j.amc.2019.04.014
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    References listed on IDEAS

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    1. Sun, HongGuang & Li, Zhipeng & Zhang, Yong & Chen, Wen, 2017. "Fractional and fractal derivative models for transient anomalous diffusion: Model comparison," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 346-353.
    2. 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.
    3. Yan, Guangwu & Zhang, Jianying, 2009. "A higher-order moment method of the lattice Boltzmann model for the Korteweg–de Vries equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(5), pages 1554-1565.
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    Cited by:

    1. Dai, Houping & Feng, Yingxin & Wei, Xuedan & Chen, Dongdong & Zheng, Zhoushun & Wang, Jianzhong, 2023. "Space fractional-order modeling for the sintering process of metal fibers via Lattice Boltzmann method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 214(C), pages 373-387.
    2. Rui Du & Jincheng Wang & Dongke Sun, 2019. "Lattice-Boltzmann Simulations of the Convection-Diffusion Equation with Different Reactive Boundary Conditions," Mathematics, MDPI, vol. 8(1), pages 1-12, December.

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