The Exponential Transformation Based Lattice Boltzmann Model for Convection-Diffusion Equation (Advances in Applied Mathematics and Mechanics, 2024)
In this paper, an exponential transformation based lattice Boltzmann (LB)model for solving the $n$-dimensional ($n{\rm D}$) convection-diffusion equation(CDE) is developed. Firstly, a class of exponential transformation is proposed to convert the $n{\rm D}$ CDE into a diffusion equation. Then, the converted diffusion equation is solved by theLB model. So, compared to the available LB models for CDE, the present LB modelcan eliminate the difficulty in treating the convection term. With the direct Taylor expansion method, it is shown that the CDE can be exactly derived from the exponentialtransformation based LB model. Finally, a variety of numerical tests have been conducted to validate the present LB model. It can be found that the numerical resultsagree well with the analytical solutions. Moreover, we also find that the present LBmodel has second-order convergence rate in space, and it is more effective and morestable than the previous LB model for the CDE.