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Updated: Jul 26, 2025

The Diffusion of Passive Tracers in Laminar Shear Flow
Published on: May 1, 2018
Fourth-order multiple-relaxation-time lattice Boltzmann model and equivalent finite-difference scheme for
Ying Chen1, Zhenhua Chai1,2,3, Baochang Shi1,3
1School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China.
Abstract:
In this paper, we first develop a fourth-order multiple-relaxation-time lattice Boltzmann (MRT-LB) model for the one-dimensional convection-diffusion equation (CDE) with the constant velocity and diffusion coefficient, where the D1Q3 (three discrete velocities in one-dimensional space) lattice structure is used. We also perform the Chapman-Enskog analysis to recover the CDE from the MRT-LB model. Then an explicit four-level finite-difference (FLFD) scheme is derived from the developed MRT-LB model for the CDE. Through the Taylor expansion, the truncation error of the FLFD scheme is obtained, and at the diffusive scaling, the FLFD scheme can achieve the fourth-order accuracy in space. After that, we present a stability analysis and derive the same stability condition for the MRT-LB model and FLFD scheme. Finally, we perform some numerical experiments to test the MRT-LB model and FLFD scheme, and the numerical results show that they have a fourth-order convergence rate in space, which is consistent with our theoretical analysis.
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