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The Exponential Transformation Based Lattice Boltzmann Model for Convection-Diffusion Equation

The Exponential Transformation Based Lattice Boltzmann Model for Convection-Diffusion Equation

Year:    2025

Author:    Ting Zhang, Shuqi Cui, Ning Hong, Baochang Shi

Advances in Applied Mathematics and Mechanics, Vol. 17 (2025), Iss. 1 : pp. 224–239

Abstract

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 the LB model. So, compared to the available LB models for CDE, the present LB model can 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 exponential transformation 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 results agree well with the analytical solutions. Moreover, we also find that the present LB model has second-order convergence rate in space, and it is more effective and more stable than the previous LB model for the CDE.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2023-0031

Advances in Applied Mathematics and Mechanics, Vol. 17 (2025), Iss. 1 : pp. 224–239

Published online:    2025-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    16

Keywords:    Lattice Boltzmann model convection-diffusion equation exponential transformation.

Author Details

Ting Zhang

Shuqi Cui

Ning Hong

Baochang Shi