A Coupled Lattice Boltzmann Model for Advection and Anisotropic Dispersion Problem in Shallow Water

Yineng Li; Ping Huang

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A Coupled Lattice Boltzmann Model for Advection and Anisotropic Dispersion Problem in Shallow Water

Yineng Li,Ping Huang *

School of Environmental Science and Engineering, Sun Yat-sen University

*Correspondence author

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Funding: 教育部博士点基金（No.20060558064）

Opened online:30 December 2008

Accepted by: none

Citation: Yineng Li,Ping Huang.A Coupled Lattice Boltzmann Model for Advection and Anisotropic Dispersion Problem in Shallow Water[OL]. [30 December 2008] http://en.paper.edu.cn/en_releasepaper/content/27110

A coupled lattice Boltzmann model(CLBM) for 2-D advection and anisotropic dis- persion equation(AADE) and shallow water equations is formulated and implemented. Multi-relaxation-time (MRT) method is used for the flow field and the L-basis two- relaxation-time (TRT) method is used for the pollutant field. The relaxation time for the antisymmetric part of the pollutant deviates from a constant for flows with variable free surface water depth. Numerical tests show that this scheme strictly obeys conserva- tion of mass and momentum. And the model has a better accuracy when zD is closer to 1/2 and ze is closer to sum(zd/9). Excellent agreement is obtained between numerical predictions and analytical solutions in pure dispersion problem and advection-dispersion problem. Comparison with finite different method indicates that the variation of the free surface water depth does not affect the mass and momentum conservation of the model and that the model has the ability to simulate complex bed topography problem. Comparison with finite volume method in the 2-D steady flow around a rectangular column with non-slip boundary shows that the LB scheme has the capacity to solve the complex advection- dispersion problems in shallow water.

Keywords:coupled lattice Boltzmann method;shallow water equation; advection and anisotropic dispersion;free surface;conservation law

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