Lattice Boltzmann Simulation of Spatial Fractional Convection–Diffusion Equation

Abstract

The space fractional advection–diffusion equation is a crucial type of fractional partial differential equation, widely used for its ability to more accurately describe natural phenomena. Due to the complexity of analytical approaches, this paper focuses on its numerical investigation. A lattice Boltzmann model for the spatial fractional convection–diffusion equation is developed, and an error analysis is carried out. The spatial fractional convection–diffusion equation is solved for several examples. The validity of the model is confirmed by comparing its numerical solutions with those obtained from other methods The results demonstrate that the lattice Boltzmann method is an effective tool for solving the space fractional convection–diffusion equation.

Keywords

• lattice Boltzmann method
• spatial fractional convection–diffusion equation
• numerical simulation
• Riemann–Liouville fractional derivative