TY - JOUR
TI - Lattice Boltzmann model for the Riesz space fractional reaction-diffusion
AU - Dai Hou-Ping
AU - Zheng Zhou-Shun
AU - Tan Wei
JN - Thermal Science
PY - 2018
VL - 22
IS - 4
SP - 1831
EP - 1843
PT - Article
AB - 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.