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

Houping Dai, Xuedan Wei, Mengjun Li and Zhoushun Zheng
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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

International Journal of Modern Physics C (IJMPC), 2023, vol. 34, issue 01, 1-11

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.

Keywords: Lévy–Feller fractional advection–diffusion equation; lattice Boltzmann method; Chapman–Enskog analysis (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0129183123500018

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