Abstract
Lattice gas automata have received considerable interest for the last several years and possibly may become a powerful numerical method for solving various partial differential equations and modeling different physical phenomena, because of their discrete and parallel nature and the capability of handling complicated boundaries. In this paper, we present recent studies on the lattice gas model for magnetohydrodynamics. The FHP-type lattice gas model has been extended to include a bidirectional random walk process, which allows well-defined statistical quantities, such as velocity and magnetic field, to be computed from the microscopic particle representation. The model incorporates a new sequential particle collision method to increase the range of useful Reynolds numbers in the model, an improvement that may also be of use in other lattice gas models. In the context of a Chapman-Enskog expansion, the model approximates the incompressible magnetic hydrodynamic equations in the limit of low Mach number and highβ. Simulation results presented here demonstrate the validity of the model for several basic problems, including sound wave and Alfvén wave propagation, and diffusive Kolmogoroff-type flows.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
U. Frisch, B. Hasslacher, and Y. Pomeau,Phys. Rev. Lett. 56:1505 (1986).
S. Wolfram,J. Stat. Phys. 45:19–74 (1986).
U. Frisch, D. d'Humières, B. Hasslacher, P. Lallemand, Y. Pomeau, and J.-P. Rivet,Complex Systems 1:649–707 (1987).
G. D. Doolen, ed.,Complex Systems 1(4):545–851 (1987). [Articles mostly based on presentations given at the Workshop on Large Nonlinear Systems, Santa Fe, New Mexico, October 27–29, 1986.]
G. D. Doolen, ed.,Lattice Gas Methods for PDEs (Addison-Wesley, 1989).
D. d'Humiéres, P. Lallemand, and G. Searby,Complex Systems 1:333–350 (1987).
D. H. Rothman and J. M. Keller,J. Stat. Phys. 52:1119–1127 (1988).
S. Chen, K. Diemer, G. D. Doolen, K. Eggert, S. Gutman, and B. J. Travis,Physica D 47:72 (1991).
S. Chen, Hudong Chen, Gary D. Doolen, S. Gutman, and M. Lee,J. Stat. Phys. 62:1121 (1991).
S. Chen, G. D. Doolen, K. Eggert, D. Grunau, and E. Y. Loh, Lattice gas simulations of one and two-phase fluid flows using the connection machine-2, inProceeding of Discrete Models of Fluid Dynamics, A. S. Aves, ed. (1991), p. 232.
D. Montgomery and G. D. Doolen,Phys. Lett. A 120:229–231 (1987).
D. Montgomery and G. D. Doolen,Complex Systems 1:831–838 (1987).
H. Chen and W. H. Matthaeus,Phys. Rev. Lett. 58:1845 (1987).
H. Chen, W. H. Matthaeus, and L. W. Klein,Phys. Fluids 31:1439–1445 (1988).
S. A. Orszag and V. Yakhot,Phys. Rev. Lett. 56:1691–1693 (1986).
L. Kadanoff, G. McNamara, and G. Zanetti,Phys. Rev. A 40:4527–4541 (1989).
S. Chen, Zhen-su She, L. C. Harrison, and G. D. Doolen,Phys. Rev. A 39:2725–2727 (1989).
S. Chen, H. Chen, G. Doolen, Y. C. Lee, H. Rose, and H. Brand,Physics D 47:97 (1991).
S. Chen, H. Chen, D. Martinéz, and W. Matthaeus, Lattice Boltzmann model for simulation of magnetohydrodynamics,Phys. Rev. Lett. (1992).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Chen, S., Martínez, D.O., Matthaeus, W.H. et al. Magnetohydrodynamics computations with lattice gas automata. J Stat Phys 68, 533–556 (1992). https://doi.org/10.1007/BF01341761
Issue Date:
DOI: https://doi.org/10.1007/BF01341761