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Approximation of the Lévy–Feller advection–diffusion process by lattice Boltzmann method

Author

Listed:
  • Houping Dai

    (College of Mathematics and Statistics, Jishou University, Jishou 416000, P. R. China)

  • Xuedan Wei

    (College of Mathematics and Statistics, Jishou University, Jishou 416000, P. R. China)

  • Mengjun Li

    (College of Mathematics and Statistics, Jishou University, Jishou 416000, P. R. China)

  • Zhoushun Zheng

    (School of Mathematics and Statistics, Central South University, Changsha 410083, P. R. China)

Abstract

In this paper, in order to expand the lattice Boltzmann method (LBM) to deal with more space-fractional systems, a fresh lattice Boltzmann scheme is proposed to approximate a Lévy–Feller advection–diffusion process, which is governed by the Lévy–Feller fractional advection–diffusion equation (LFADE). First, the fractional integral operator is discretized and the LFADE is transformed into a standard equation. Second, combining with Taylor expansion and Chapman–Enskog analysis, a family of the LFADE is recovered correctly from the continuous Boltzmann equation through selecting the equilibrium distribution functions. Finally, some test examples are presented and it is found that the numerical results agree well with the analytical solutions. In addition, the result in terms of stability is also tested by comparing with previous studies.

Suggested Citation

  • Houping Dai & Xuedan Wei & Mengjun Li & Zhoushun Zheng, 2023. "Approximation of the Lévy–Feller advection–diffusion process by lattice Boltzmann method," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 34(01), pages 1-11, January.
    • Handle: RePEc:wsi:ijmpcx:v:34:y:2023:i:01:n:s0129183123500018
    DOI: 10.1142/S0129183123500018
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