Variably saturated flow described with the anisotropic Lattice Boltzmann methods

Computers and Fluids

Volumn 35, Issue 8-9, 2006, Pages 831-848

  Ginzburg, Irina ^a  

^a CEMAGREF   (France)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; DIFFUSION; DISPERSIONS; EIGENVALUES AND EIGENFUNCTIONS; INTEGRAL EQUATIONS; NONLINEAR EQUATIONS; NUMERICAL ANALYSIS; STATISTICAL METHODS;

INTEGRAL TRANSFORMS; LATTICE BOLTZMANN METHODS; SATURATED FLOW;

ANISOTROPY;

ANISOTROPY; BOUNDARY CONDITIONS; DIFFUSION; DISPERSIONS; EIGENVALUES AND EIGENFUNCTIONS; INTEGRAL EQUATIONS; NONLINEAR EQUATIONS; NUMERICAL ANALYSIS; STATISTICAL METHODS;

EID: 33646946487     PISSN: 00457930     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compfluid.2005.11.001     Document Type: Article

References (28)

1. Brooks RH, Corey AT. Hydraulic properties of porous media, Hydrol Pap, 3, Colo. State Univ., Fort Collins, 1964.
2. Celia M., Bouloutas E., and Zabra R. A general mass-conservative numerical solution for the unsaturated flow equation. Water Resour Res 26 (1990) 1483-1496
3. Clement T.P., Wise W., Molz F.J., and Wen M. A comparison of modeling approaches for steady-state unconfined flow. J Hydrol 181 (1996) 189-209
4. d'Humières D. Generalized Lattice-Boltzmann equations. AIAA rarefied gas dynamics: theory and simulations. Progr Astronaut Aeronaut 59 (1992) 450-548
5. d'Humières D., Bouzidi M., and Lallemand P. Thirteen-velocity three-dimen-sional lattice Boltzmann model. Phys Rev E 63 (2001) 066702-1-066702-7
6. d'Humières D., Ginzburg I., Krafczyk M., Lallemand P., and Luo L.-S. Multiple-relaxation-time lattice Boltzmann models in three dimensions. Phil Trans R Soc Lond A 360 (2002) 437-451
7. d'Humières D, Ginzburg I. Some stability results for Lattice Boltzmann advection-diffusion equations, in preparation.
8. Ginzburg I., and d'Humières D. Multi-reflection boundary conditions for lattice Boltzmann models. Phys Rev E 68 (2003) 066614-1-066614-30
9. Ginzburg I., Carlier J.-P., and Kao C. Lattice Boltzmann approach to Richards' equation. In: Miller C.T. (Ed). Computational methods in water resources. Proceedings of the CMWR XV, June 13-17 (2004), Elsevier, Chapel Hill, NC, USA 583-597
10. Ginzburg I. Equilibrium-type and Link-type Lattice Boltzmann models for generic advection and anisotropic-dispersion equation. Adv Water Resour 28 (2005) 1171-1195
11. Ginzburg I. Generic boundary conditions for Lattice Boltzmann models and their application to advection and anisotropic-dispersion equations. Adv Water Resour 28 (2005) 1196-1216
12. Kao C., Bouarfa S., and Zimmer D. Steady state analysis of unsaturated flow above a shallow water-table aquifer drained by ditches. J Hydrol 250 (2001) 122-133
13. Lallemand P., and Luo L.-S. Theory of the lattice Boltzmann method: Dispersion, dissipation, isotropy, Galilean invariance, and stability. Phys Rev E 61 (2000) 6546-6562
14. Marinelli F., and Durnford D.S. Semianalytical solution to Richards' equation for layered porous media. J Irrigat Drainage Eng 124 6 (1998) 290-299
15. Miller C.T., Williams G.A., Kelly C.T., and Tocci M.D. Robust solution of Richard's equation for nonuniform porous media. Water Resour Res 34 (1998) 2599-2610
16. Miller C.T., Abhishek C., Sallerson A.B., Prins J.F., and Farthing M.W. A comparison of computational and algorithmic advances for solving Richards' equation. In: Miller C.T. (Ed). Computational methods in water resources. Proceedings of the CMWR XV, June 13-17 vol. 2 (2004), Elsevier, Chapel Hill, NC, USA 1131-1145
17. Mualem Y. A new model for predicting the hydraulic conductivity of unsaturated porous media. Water Resour Res 12 (1976) 513-522
18. Qian Y., d'Humières D., and Lallemand P. Lattice BGK models for Navier-Stokes equation. Europhys Lett 17 (1992) 479-484
19. Ross P.J. Efficient numerical methods for infiltration using Richard's equation. Water Resour Res 26 (1990) 279-290
20. Vander Sman R.G.M., and Ernst M.H. Convection-diffusion Lattice Boltzmann scheme for irregular lattices. J Comput Phys 160 (2000) 766-782
21. Short D., Dawes W.R., and White I. The practicability of using Richard's equation for general purpose soil water dynamics models. Environ Int 21 5 (1995) 723-730
22. Vogel T., van Genuchten M.Th., and Cislerova M. Effect of the shape of the soil hydraulic functions near saturation on variably saturated flow predictions. Adv Water Resour 24 (2001) 133-144
23. vanGenuchten M.Th. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci Soc Am J Proc 44 (1980) 892-898
24. Williams G.A., and Miller C.T. An evaluation of temporally adaptive transformation approaches for solving Richards' equation. Adv Water Resour 22 (1999) 831-840
25. Williams G.A., Miller C.T., and Kelly C.T. Transformation approaches for simulating flow in variably saturated porous media. Water Resour Res 4 (2000) 923-934
26. Wolf-Gladrow D. Lattice gas cellular automata and lattice Boltzmann models: an introduction. Lecture notes in mathematics 1725 (2000), Springer
27. Zhang X., Bengough A.G., Deeks L.K., Crawford J.W., and Young I.M. A lattice BGK model for advection and anisotropic dispersion equation. Adv Water Resour 25 (2002) 1-8
28. Zhang X., Bengough A.G., Deeks L.K., Crawford J.W., and Young I.M. A novel three-dimensional lattice Boltzmann model for solute transport in variably saturated porous media. Water Resour Res 38 (2002) 1-10