×

Extended hybrid pressure and velocity boundary conditions for D3Q27 lattice Boltzmann model. (English) Zbl 1243.76078

Summary: The extended hybrid electronic-ionic, thermal, magnetic, electric and force couple fields pressure and velocity boundary conditions for D3Q27 lattice Boltzmann model is established. Then, the closed-form solutions of extended distribution functions are derived. Last, the Fukushima nuclear plant Cesium-137 penetration case is discussed.

MSC:

76M28 Particle methods and lattice-gas methods
Full Text: DOI

References:

[1] Zhan, J. M.; Luo, Y. Y.; Li, Y. S., A high accuracy hybrid method for two-dimensional Navier-Stokes equations, Appl. Math. Model., 32, 873 (2008) · Zbl 1187.76722
[2] Qian, Y. H.; D’Humières, D.; Lallemand, P., Lattice BGK models for Navier-Stokes equation, Europhys. Lett., 17, 479 (1992) · Zbl 1116.76419
[3] Zou, Q.; Hou, S.; Chen, S.; Doolen, G. D., A improved incompressible lattice Boltzmann model for time-independent flows, J. Stat. Phys., 81, 35 (1995) · Zbl 1106.82366
[4] Guo, Z.; Shi, B.; Wang, N., Lattice BGK model for incompressible Navier-Stokes equation, J. Comput. Phys., 165, 288 (2000) · Zbl 0979.76069
[5] Noble, D. R.; Chen, S.; Georgiadis, J. G., A consistent hydrodynamic boundary condition for the lattice Boltzmann method, Phys. Fluids, 7, 203 (1995) · Zbl 0846.76086
[6] Chen, S.; Martı´nez, D.; Mei, R., On boundary conditions in lattice boltzmann methods, Phys. Fluids, 8, 2527 (1996) · Zbl 1027.76630
[7] Chen, S.; Doolen, G. D., lattice boltzmann method for fluid flows, Annu. Rev. Fluid Mech., 30, 329 (1998) · Zbl 1398.76180
[8] J. Bear, The transition zone between fresh and salt waters in coastal aquifers, Ph.D thesis 1960; Berkeley, University of California.; J. Bear, The transition zone between fresh and salt waters in coastal aquifers, Ph.D thesis 1960; Berkeley, University of California.
[9] Zou, Q. S.; He, X. Y., On pressure and velocity boundary conditions for the lattice Boltzmann BGK model, Phys. Fluids, 9, 1591 (1997) · Zbl 1185.76873
[10] Maier, R. S.; Bernard, R. S.; Grunau, D. W., Boundary conditions for the lattice Boltzmann method, Phys. Fluids, 8, 1788 (1996) · Zbl 1027.76632
[11] Noble, D. R.; Chen, S. Y.; Georgiadis, J. G.; Buckius, R. O., A consistent hydrodynamic boundary-condition for the lattice Boltzmann method, Phys. Fluids, 7, 203 (1995) · Zbl 0846.76086
[12] Gary, D.; Doolen, Lattice gas methods: theory, applications, and hardware (1991), MIT Press: MIT Press Cambridge, Mass.
[13] He, X. Y.; Doolen, G. D., Thermodynamic foundations of kinetic theory and Lattice Boltzmann models for multiphase flows, J. Stat. Phys., 107, 309 (2002) · Zbl 1007.82020
[14] Gary, D.; Doolen; Frisch, M.; Hasslacher, B.; Orszag, S.; Wolfram, S., Lattice gas methods for partial differential equations (1990), Addison-Wesley: Addison-Wesley Redwood City, California, Wokingham, 4 · Zbl 0718.00017
[15] Zhang, H. I.; Hu, S. D.; Wang, G. L.; Zhu, J. Y., Modeling and simulation of plasma jet by lattice Boltzmann method, Appl. Math. Model., 31, 1124 (2007) · Zbl 1141.76048
[16] Chai, Z. H.; Shi, B. C., A novel lattice Boltzmann model for the poisson equation, Appl. Math. Model., 32, 2050 (2008) · Zbl 1145.82344
[17] Frisch, U.; Hasslacher, B.; Pomeau, Y., Lattice-gas automata for the Navier-Stokes equation, Phys. Rev. Lett., 56, 1505 (1986)
[18] Jeremy, R.; Henderson; Ian, G.; Main; Calum, M.; Michael, G.; Norman, A fracture-mechanical cellular automaton model of seismicity, Pure Appl. Geophys., 142, 545 (1994)
[19] He, X. Y.; Luo, L. S., Theory of the lattice Boltzmann method: from the Boltzmann equation to the lattice Boltzmann equation, Phys. Rev. E, 56, 6811 (1997)
[20] He, X. Y.; Luo, L. S., Lattice Boltzmann model for the incompressible Navier-Stokes equation, J. Stat. Phys., 88, 927 (1997) · Zbl 0939.82042
[21] Guo, Z. L.; Shi, B. C.; Wang, N. C., Lattice BGK model for incompressible Navier-Stokes equation, J. Comput. Phys., 165, 288 (2000) · Zbl 0979.76069
[22] Zhu, B.; Qin, T., Hypersingular integral equation method for a three-dimensional crack in anisotropic electro-magneto-elastic bimaterials, Theor. Appl. Fract. Mech., 47, 219 (2007)
[23] Zhu, B.; Qin, T., 3D modeling of crack growth in electro-magneto-thermo-elastic coupled viscoplastic multiphase composites, Appl. Math. Model., 33, 1014 (2009) · Zbl 1168.74442
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.