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LATTICE BOLTZMANN MODEL FOR THE RIESZ SPACE FRACTIONAL REACTION-DIFFUSION

ABSTRACT
In this paper, a Riesz space fractional reaction-diffusion equation with non-linear source term is considered on a finite domain. This equation is commonly used to describe anomalous diffusion in thermal science. To solve the diffusion equation, a new fractional lattice Boltzmann method is proposed. Firstly, a difference approximation for the global spatial correlation of Riesz fractional derivative is derived by applying the numerical discretization technique, and a brief convergence analysis is presented. Then the global spatial correlation process is inserted into the evolution process of the standard lattice Boltzmann method. With combining Taylor expansion, Chapman-Enskog expansion and the multi-scales expansion, the governing evolution equation is recovered from the continuous Boltzmann equation. Three numerical examples are provided to confirm our theoretical analysis and illustrate the effectiveness of our method at last.
KEYWORDS
PAPER SUBMITTED: 2017-09-05
PAPER REVISED: 2017-09-28
PAPER ACCEPTED: 2017-09-28
PUBLISHED ONLINE: 2018-09-10
DOI REFERENCE: https://doi.org/10.2298/TSCI1804831D
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2018, VOLUME 22, ISSUE 4, PAGES [1831 - 1843]
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© 2018 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence