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Research Papers

Lattice Boltzmann Method for Advection and Anisotropic Dispersion Equation

[+] Author and Article Information
Jian Guo Zhou

School of Engineering, University of Liverpool, Liverpool L69 3GQ, UKj.g.zhou@liverpool.ac.uk

J. Appl. Mech 78(2), 021007 (Nov 08, 2010) (5 pages) doi:10.1115/1.4002572 History: Received November 30, 2009; Revised September 10, 2010; Published November 08, 2010; Online November 08, 2010

A lattice Boltzmann method is developed for the solution of the advection and anisotropic dispersion equation. In the approach, a novel local equilibrium distribution function is formulated to preserve the advantage of using a single relaxation time for the recovery of the isotropic or anisotropic dispersion tensor in the equation. The method fully retains the innate kinetic features and the simple procedure of the standard lattice Boltzmann method, with an additional benefit of being suitable for rectangular lattices at little extra computational cost. The model has been verified and the results have shown that it can produce accurate solutions with great potential to general advection and dispersion problems, leading to broad applications within a variety of interdisciplinary areas.

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Figures

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Figure 2

1D Gaussian hills from top to bottom for (a) Pe=0.5, (b) Pe=1, and (c) Pe=5

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Figure 3

2D isotropic Gaussian hills from top to bottom for (a) Pe=0.5, (b) Pe=1, and (c) Pe=5

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Figure 1

Nine-velocity rectangular lattice (D2Q9)

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Figure 4

Prediction of an anisotropic Gaussian hill

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Figure 5

Migration of chloride ion

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Figure 6

Transport of multiple point sources in complex flow

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Figure 7

Nineteen-velocity cuboid lattice (D3Q19)

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