The Numerical Solution of Richards Equation Using the Lattice Boltzmann Method

Ning Ning Liu

doi:10.4028/www.scientific.net/AMM.188.90

Paper Titles

Numerical Study of the Influence of Interlayer Mechanical Properties on Salt Cavern Storage Stability
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Study on the Evaluation Method of Subgrade Settlement Caused by Structure Layer of the High-Speed Railway
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Study on Triaxial Creep Experiment of Beishan Granite under Low Confining Pressures
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Determination of Ultimate Filling Height of Slag Subgrade with FEM Modelling
p.84

The Numerical Solution of Richards Equation Using the Lattice Boltzmann Method
p.90

Research on the Cavern Stability and Rock Fracture with Different Joint Groups
p.96

Study on the Mechanisms of Hydraulic Fracturing Crack Initiation and Propagating
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Quasi-Static Test of Reinforced Concrete Shear Wall with Low Concrete Strength and Reinforcement Ratio
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The Effect to Structure due to SSI
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HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vol. 188The Numerical Solution of Richards Equation Using...

The Numerical Solution of Richards Equation Using the Lattice Boltzmann Method

Abstract:

The Richards equation is applied to describe the unsaturated soil moisture movement. The Lattice Boltzmann method is developed to solve this partial differential equation. The accuracy and efficiency of the Lattice Boltzmann method in modeling unsaturated soil moisture movement are compared to the Philip series method as well as Crank-Nicolson finite difference scheme. The results reveal that all three methods provide solutions of comparable accuracy. The computation efficiency, accuracy and simplicity of the Lattice Boltzmann method indicate that it has the capacity to model unsaturated soil moisture movement.

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Applied Mechanics and Materials (Volume 188)

Pages:

90-95

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.188.90

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Online since:

June 2012

Authors:

Ning Ning Liu

Keywords:

Crank-Nicolson Finite Difference Scheme, Lattice Boltzmann Method, Philip Series Method, Richards Equation, Unsaturated Infiltration

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References

[1] Ghidaoui MS, Deng JQ, Xu K, et al. A Boltzmann based model for open channel flows, Int J Number Meth Fluids. 2001, 35: 449-494.

DOI: 10.1002/1097-0363(20010228)35:4<449::aid-fld106>3.0.co;2-f

Google Scholar

[2] J. Zhang, G. Yan. Lattice Boltzmann method for one and two dimensional Burgers equation, Physica A, (2008).

Google Scholar

[3] Chen S. Y, Doolen G.D. Lattice Boltzmann method for fluid flows, Annu. Fluid Mech., 1998, (3): 314-322.

DOI: 10.1146/annurev.fluid.30.1.329

Google Scholar

[4] Brooks R H, Corey A T. Hydraulic properties of porous media, Fort Collins: Colorado State University, 1964, 3-27.

Google Scholar

[5] Bhatnagar P L, Gross E P, Krook M K. A model for collision processes in gases. I: small amplitude processes in charged and neutral one-component system, Phys. Rev., 1954, (94): 511-525.

DOI: 10.1103/physrev.94.511

Google Scholar

[6] Qian Y, d'Humieres D, Lallemand P. Lattice BGK model for Navier-Stokes equation, Europhys. Lett. 1992, (17): 479-484.

DOI: 10.1209/0295-5075/17/6/001

Google Scholar

[7] Wolf-Gladrow D A. Lattice-gas Cellular Automata and Lattice Boltzmann Models: An Introduction, New York Springer, (2000).

DOI: 10.1007/978-3-540-46586-7_3

Google Scholar

[8] Lei ZhiDong, Yang ShiXiu, Xie SenChuan. Soil Water Dynamic, Beijing, Tsinghua University Press, (1988).

Google Scholar

[9] J. Crank, P. Nicolson. A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type, Mathematical Proceedings of the Cambridge Philosophical Society. 1947, 43(1): 50-67.

DOI: 10.1017/s0305004100023197

Google Scholar