Lattice Boltzmann method for tempered space-fractional advection-diffusion equation with applications to tempered fractional transport

Advection−diffusion phenomena are widespread in numerous scientific and engineering disciplines. However, the classical advection−diffusion equation is often insufficient to capture the inherent complexities of these phenomena. In contrast, the space-fractional advection−diffusion equation (SFADE) and its extension, the tempered SFADE, offer more accurate descriptions. Despite the development of several traditional numerical methods to solve the tempered SFADE, employing the lattice Boltzmann method (LBM) to solve it remains a significant challenge. In this study, we propose a novel LBM tailored for the tempered SFADE. By utilizing Maxwell iteration method, we demonstrate that the LBM recovers the target equation with second-order accuracy. Three numerical examples validate the effectiveness and convergence order. The proposed LBM is employed to simulate a point-source release and explore tempered fractional diffusion characteristics. This work provides a new numerical tool, promoting the wider application of the tempered SFADE in science and engineering.