Numerical simulation of the fractional dispersion advection equations based on the lattice Boltzmann model
type: Item
instance of: scholarly article
title: Numerical simulation of the fractional dispersion advection equations based on the lattice Boltzmann model
zbMATH Open document ID: 1459.76105
DOI: 10.1155/2020/2570252
author: Boyu Wang
author: Jianying Zhang
author: Guangwu Yan
published in: Mathematical Problems in Engineering
publication date: 2020-10-14T00:00:00Z
review text: Summary: The fractional dispersion advection equations (FDAEs) have recently attracted considerable attention due to their extensive application in the fields of science and engineering. For example, it has been shown that the anomalous solute transport behaviour that exists in hydrology can be well explained by introducing FDAEs. Therefore, the study of FDAEs has profound significance for understanding real transport phenomena in nature. Nevertheless, the existing algorithms for the FDAEs are generally intricate and costly. Therefore, exploiting an efficient solution technique has been a concern for scientists. In an effort to overcome this challenge, a promising lattice Boltzmann (LB) model for the FDAEs is presented in this paper. The Riemann-Liouville definition and the Grünwald-Letnikov definition are introduced for the time derivatives. In addition, Chapman-Enskog analysis is applied to recover the FDAEs. To test the validity of the model, three numerical examples are carried out. In addition, a comparative study of the proposed model and the classical implicit finite difference scheme is also conducted. The numerical results show that the model is suitable for simulating FDAEs.
Mathematics Subject Classification ID: 76M28
Mathematics Subject Classification ID: 65M75
zbMATH DE Number: 7260840
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2020/2570252
OpenAlex ID: W3086268534
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description: scientific article; zbMATH DE number 7260840