On Complex Boundary Conditions of the Lattice Boltzmann Method for the Diffusion Equations

HUANG Jun-tao; ZHANG Li; YONG Wen-an; WANG Mo-ran

doi:10.3879/j.issn.1000-0887.2014.03.009

Volume 35 Issue 3

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Article Navigation > Applied Mathematics and Mechanics > 2014 > 35(3): 305-312

HUANG Jun-tao, ZHANG Li, YONG Wen-an, WANG Mo-ran. On Complex Boundary Conditions of the Lattice Boltzmann Method for the Diffusion Equations[J]. Applied Mathematics and Mechanics, 2014, 35(3): 305-312. doi: 10.3879/j.issn.1000-0887.2014.03.009

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On Complex Boundary Conditions of the Lattice Boltzmann Method for the Diffusion Equations

doi: 10.3879/j.issn.1000-0887.2014.03.009

¹Department of Engineering Mechanics, School of Aerospace,Tsinghua University, Beijing 100084, P.R.China;²Zhou PeiYuan Center for Applied Mathematics, Tsinghua University, Beijing 100084, P.R.China

Funds: The National Natural Science Foundation of China(51176089); The National Basic Research Program of China (973 Program)(2013CB228301)

Received Date: 2013-09-25
Rev Recd Date: 2013-12-17
Publish Date: 2014-03-15

Abstract

Abstract

The diffusion equation with the third-type boundary condition solved by the lattice Boltzmann method was theoretically and numerically studied. A new numerical algorithm based on the bounce-back method was constructed, to deal with the complex boundary problem. By asymptotic analysis, the compatibility of the numerical method was proved. The accuracy and stability of the algorithm were discussed via several numerical examples. Compared with the previous work, this numerical approach makes a significant improvement in the aspects of accuracy, stability and efficiency. Finally, through the numerical example of a reaction-diffusion problem with complex boundary, feasibility and effectiveness of the presented method are proved in the simulation of the multi-physical and chemical transport process in porous medium.
- lattice Boltzmann method,
- diffusion equation,
- third-type boundary condition,
- asymptotic analysis,
- complex boundary

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References(19)

References

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