Abstract
In this paper, we propose new lattice BGK models for one-, two- and three-dimensional thermohydrodynamics. A proper internal energy is introduced and the energy equation is obtained. The derivation of the thermohydrodynamic equations is systematic and numerical simulations are carried out to verify the theoretical values of the sound speed, the shear viscosity and the conductivity. One-dimensional shock-tube problem and two-dimensional Rayleigh-Bénard convection are simulated. Good performance and satisfactory results are obtained. These models can be applied to many interesting cases, in particular, the transonic regimes where the compressibility can not be neglected.
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References
Bhatnagar, P., Gross, E. P., and Krook, M. K. (1954).Phys. Rev. 94, p. 511.
Boghosian, B., and Levermore, D. (1987).Complex Sys. 1, 17.
Chapman, S., and Cowling, T. G. (1970).The Mathematical Theory of Nonuniform Gases, Cambridge University Press.
Chen, H. D., Chen, S. Y., and Matthaeus, W. (1992).Physics Review A 45, R5339.
Chen, H. D., and Matthaeus, W. (1987).Phys. Rev. Lett. 58, 1235.
Dahlburg, J. P., Montgomery, D., and Doolen, G. (1987).Phys. Rev. A36, 2471.
d'Humières, D., Lallemand, P., and Frisch, U. (1986).Europhys. Lett. 2, 291.
d'Humières, D., Lallemand, P., and Qian, Y. H. (1989).C. R. Acad. Sci. Paris. Série II 308, 585.
d'Humières, D., Qian, Y. H., and Lallemand, P. (1989).Proc. of Workshop: Discrete Kinematic Theory, Lattice Gas Dynamics and Foundations of Hydrodynamics, R. Monaco (ed.) (World Scientific), p. 192.
Doolen, G. (1991). (Ed.), Proceedings of Los Alamos Workshop, September 6–9,Physica D47.
Frisch, U., d'Humières, D., Hasslacher, B., Lallemand, P., Pomeau, Y., and Rivet, J. P. (1987).Complex Sys. 1, 649.
Frisch, U., Hasslacher, B., and Pomeau, Y. (1986).Phys. Rev. Lett. 56, 1505.
Harris, S. (1971).An Introduction to the Theory of the Boltzmann Equation, Holt, Rinehart and Winston Press.
Higuera, F., Succi, S., and Benzi, R. (1989).Europhys. Lett. 9, 663.
Kadanoff, L., McNamara, G., and Zanetti, G. (1989).Phys. Rev. 40A, 4527–4541.
McNamara, G., and Alder, B. (preprint).
McNamara, G., and Zanetti, G. (1988).Phys. Rev. Lett. 61, 2332.
Orszag, S. A., and Yakhot, V. (1986).Phys. Rev. Lett. 56, 1691.
Qian, Y. H. (1990). Lattice Gas and Lattice Kinetic Theory Applied to the Navier-Stokes Equation, Doctoral Thesis, University of Paris 6 and École Normale Supérieure.
Qian, Y. H., d'Humières, D., and Lallemand, P. (1991).Advances in Kinetic Theory and Continuum Mechanics, Book in honor of H. Cabannes, R. Gatignol and Soubbaramayer (eds.), Springer-Verlag, p. 127.
Qian, Y. H., d'Humières, D., and Lallemand, P. (1992).Europhys. Lett. 17(6), 479.
Qian, Y. H., and Orszag, S. A. (1993).Europhys. Lett. 21(3), 255–259.
Qian, Y. H., and Orszag, S. A. (in preparation).
Qian, Y. H., Sterling, J., and Chen, S. Y. (to be published).
Rivet, J. P. (1988). Hydrodynamique par la méthode de Gaz sur Réseaux, Doctoral Thesis, University of Nice and École Normale Supérieure.
Rothman, D. (1990).Journal of Geophysical Research 95, 8663.
Tilgner, A., Belmonte, A., and Libchaber, A. (to be published).
Zaleski, S. (1989).Proc. of the Workshop Cellular Automata and Modeling of Complex Physical Systems, Les Houches, France, Feb. 21–March 1, Springer-Verlag.
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Qian, Y.H. Simulating thermohydrodynamics with lattice BGK models. J Sci Comput 8, 231–242 (1993). https://doi.org/10.1007/BF01060932
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DOI: https://doi.org/10.1007/BF01060932