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.

Lattice-Boltzmann-Method-Based Numerical Simulation for Heavy Metal Migration Process during Deep-Sea Mining

“…So, the LBM is used to study the mechanism of various complex phenomena, and it has been widely used in fluid mechanics, engineering simulation, material engineering, and environmental engineering [21][22][23][24][25]. The LBM is extensively of interest by scholars who research mathematical and physical equations, such as convectiondiffusion equations, diffusion equations, and fractional Cahn-Hilliard equations [26][27][28][29][30]. Therefore, the LBM can be adopted to solve the model for describing the dissolution and transportation of heavy metal pollutants during deep-sea mining.…”

Lattice Boltzmann Method-based Numerical Simulation for Heavy Metal Migration Process during Deep-sea Mining

“…So, LBM is used to study the mechanism of various complex phenomena, and it has been widely used in the engineering simulation, fluid mechanics, material engineering and environmental engineering [16][17][18][19]. LBM particularly is extensively concerned by scholars who research the mathematical and physical equations as convection-diffusion equations, diffusion equations, fractional Cahn-Hilliard equations [20][21][22][23]. Therefore, LBM can be adopted to solve the model for describing the dissolution and transportation of heavy metals pollutants during deep-sea mining.…”

Variational approach to fractal reaction-diffusion equations with fractal derivatives

“…Recently Mahalakshmi et al [1] studied a non-linear reaction-diffusion equation arising in biomedicine, and an accurate solution was obtained. The dimensionless material balance of substrate inside the support in a solid of planar or spherical shape can be written [1][2][3][4]:…”