Third order equivalent equation of lattice Boltzmann scheme

Discrete and Continuous Dynamical Systems

Volumn 23, Issue 1-2, 2009, Pages 221-248

  Dubois, François ^a,b  

^a UNIVERSITÉ PARIS SACLAY   (France)

^b University of Paris Cité   (France)

Author keywords

Acoustics; Lattice Boltzmann; Taylor formula; Thermies

Indexed keywords

EID: 60949092668     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.2009.23.221     Document Type: Article

References (30)

1. P. Bhatnagar, E. Gross and M. Krook, A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems, Physical Review, 94 (1954), 511-525.
2. J. Broadwell, Study of a rarefied shear flow by the discrete velocity method, Journal of Fluid Mechanics, 19 (1964), 401-414.
3. H. Cabannes, Etude de la propagation des ondes dans un gaz à 14 vitesses, Journal de Mécanique, 14 (1975), 705-744.
4. T. Carleman, "Problèmes Mathématiques dans la Théorie Cinétique des Gaz," Almqvist & Wiksell, Uppsala, 1957.
5. S. Chapman and T. G. Cowling, "The Mathematical Theory of Non-Uniform Gases," Cambridge University Press, Cambridge, 1939.
6. S. Chen and G. D. Doolen, Lattice Boltzmann method for fluid flows, Annual Review of Fluid Mechanics, 30 (1998), 329-364.
7. Y. Chen, H. Ohashi and M. Akiyama, Thermal lattice Bhatnagar-Gross-Krook model without nonlinear deviations in macrodynamic equations, Physical Review E, 50 (1994), 2776-2783.
8. D. D'Humières, Generalized Lattice-Boltzmann equations, in "Rarefied Gas Dynamics: Theory and Simulations," AIAA Progress in Astronautics and Astronautics, 159 (1992), 450-458.
9. D. D'Humières, I. Ginzburg, M. Krafczyk, P. Lallemand and L. S. Luo, Multiple-relaxation-time lattice Boltzmann models in three dimensions, Discrete modelling and simulation of fluid dynamics (Corse, 2001), R. Soc. Lond. Philos. Trans. Ser. A Math. Phys. Eng. Sci., 360 (2002), 437-451.
10. D. D'Humières, P. Lallemand and U. Frisch, Lattice gas models for 3D-hydrodynamics, Europhysics Letters, 2 (1986), 291-297.
11. F. Dubois, Une introduction au schéma de Boltzmann sur réseau, ESAIM: Proceedings, 18 (2007), 181-215.
12. F. Dubois, Equivalent partial differential equations of a Boltzmann scheme, Computers and mathematics with applications, 55 (2008), 1441-1449.
13. U. Frisch, B. Hasslacher and Y. Pomeau, Lattice gas automata for the Navier Stokes equation, Physical Review Letters, 56 (1986), 1505-1508.
14. M. Gardner, The fantastic combinations of John Conway's new solitaire game "life", Scientific American, 223 (1970), 120-123.
15. R. Gatignol, "Théorie Cinétique des gaz à Répartition Discrète de Vitesses," Lecture Notes in Physics, 36, Springer Verlag, Berlin, 1975.
16. I. Ginzburg, Equilibrium-type and link-type lattice Boltzmann models for generic advection and anisotropic-dispersion equation, Advances in Water resources, 28 (2005), 1171-1195.
17. J. Hardy, Y. Pomeau and O. De Pazzis, Time evolution of a two-dimensional classical lattice system, Physical Review Letters, 31 (1973), 276-279.
18. M. Hénon, Viscosity of a Lattice Gas, Large nonlinear systems (Santa Fe, NM, 1986), Complex Systems, 1 (1987), 763-789.
19. F. Higuera, S. Succi and R. Benzi, Lattice gas dynamics with enhanced collisions, Europhysics Letters, 9 (1989), 663-668.
20. M. Junk and M. Rheinländer, Regular and multiscale expansions of a lattice Boltzmann method, Proceedings of Computational Fluid Dynamics, 8 (2008), 25-37.
21. P. Lallemand and L.-S. Luo, Theory of the lattice Boltzmann method: Dispersion, dissipation, isotropy, Galilean invariance, and stability, Physical Review E, 61 (2000), 6546-6562.
22. P. Lallemand and L.-S. Luo, Theory of the lattice Boltzmann method: Acoustic and thermal properties in two and three dimensions, Physical Review E, 68 (2003).
23. A. Lerat and R. Peyret, Noncentered schemes and shock propagation problems, Internat. J. Computers and Fluids, 2 (1974), 35-52.
24. G. Mc Namara and G. Zanetti, Use of Boltzmann equation to simulate lattice gas automata, Physical Review Letters, 61 (1988), 2332-2335.
25. Y. H. Qian, D. D'Humières and P. Lallemand, Lattice BGK for Navier-Stokes equation, Europhysics Letters, 17 (1992), 479-484.
26. R. Rubinstein, Symmetry properties of discrete velocity sets, in "Third ICMMES Conference," Hampton, Virginia, July 2006.
27. X. Shan, Simulation of Rayleigh-Bénard convection using a lattice Boltzmann method, Physical Review E, 55 (1997), 2780-2788.
28. S. Ulam, On some mathematical problems connected with patterns of growth of figures, J. Proc. Symp. Applied Math., 14 (1962), 215-224.
29. J. Von Neumann, The general and logical theory of automata, in "Cerebral Mechanisms in behavior: The Hixon symposium" [originally presented in September 1948] (ed. L. A. Jeffress), John Wiley and Sons, New York (1951), 1-41.
30. R. F. Warming and B. J. Hyett, The modified equation approach to the stability and accuracy analysis of finite difference methods, Journal of Computational Physics, 14 (1974), 159-179.