Fully Lagrangian and Lattice Boltzmann Methods for the Advection-Diffusion Equation

Authors:
Z. L. Guo;B. C. Shi;N. C. Wang
Affiliations:
Department of Mathematics, Huazhong University of Science and Technology, Whuhan, 430074, People's Republic of China;Department of Mathematics, Huazhong University of Science and Technology, Whuhan, 430074, People's Republic of China;Department of Mathematics, Huazhong University of Science and Technology, Whuhan, 430074, People's Republic of China
Venue:
Journal of Scientific Computing
Year:
1999

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Abstract

In the last decade or so, the Lattice–Boltzmann method (LBM) has achieved great success in computational fluid dynamics. The Fully–Lagrangian method (FLM) is the generalization of LBM for conservation systems. LBM can also be developed from FLM. In this paper a FL model and a LB model are developed for D-dimensional advection-diffusion equation. The LB model can be viewed as an improved version of the FL model. Numerical results of simulation of 1-dimensional advection-diffusion equation are presented. The numerical results are found to be in good agreement with the analytic solution.