Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-26T20:33:00.569Z Has data issue: false hasContentIssue false
  • English
  • Français

Cross Correlators and Galilean Invariance in Fluctuating Ideal Gas Lattice Boltzmann Simulations

Published online by Cambridge University Press:  20 August 2015

Goetz Kaehler  and
Alexander Wagner
Goetz Kaehler*
Affiliation:
Department of Physics, North Dakota State University, Fargo, ND 58108, USA
Alexander Wagner*
Affiliation:
Department of Physics, North Dakota State University, Fargo, ND 58108, USA
*
Corresponding author.Email:goetz.kaehler@ndsu.edu
Email:alexander.wagner@ndsu.edu
Get access

Abstract

We analyze the Lattice Boltzmann method for the simulation of fluctuating hydrodynamics by Adhikari et al. [Europhys. Lett., 71 (2005), 473-479] and find that it shows excellent agreement with theory even for small wavelengths as long as a stationary system is considered. This is in contrast to other finite difference and older lattice Boltzmann implementations that show convergence only in the limit of large wavelengths. In particular cross correlators vanish to less than 0.5%. For larger mean velocities, however, Galilean invariance violations manifest themselves.

Keywords

47.11.-j47.11.Qr05.40.-aLattice BoltzmannfluctuationsGalilean invariance
Type
Research Article
Information
Communications in Computational Physics , Volume 9 , Issue 5 , May 2011 , pp. 1315 - 1322
Copyright
Copyright © Global Science Press Limited 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Adhikari, R., Stratford, K., Cates, M. E., and Wagner, A. J., Fluctuating lattice Boltzmann, Eu-rophys. Lett., 71 (2005), 473–479.Google Scholar
[2]Ihle, T., and Kroll, D. M., Stochastic rotation dynamics: a Galilean-invariant mesoscopic model for fluid flow, Phys. Rev. E., 63 (2001), 020201.Google Scholar
[3]Frisch, U., Hasslacher, B., and Pomeau, Y., Lattice-gas automata for the Navier-Stokes equation, Phys. Rev. Lett., 56 (1986), 1505–1508.CrossRefGoogle ScholarPubMed
[4]Allen, M. P., and Tildesley, D. J., Computer Simulation of Liquids, Clarendon, Oxford, 1987.Google Scholar
[5]Lifshitz, E. M., and Pitaevskii, L. P., Course of Theoretical Physics, Vol. 9, Statistical Physics, Part 2, Pergamon Press, Oxford, 1980.Google Scholar
[6]Donev, A., Vanden-Eijnden, E., Garcia, A. L., and Bell, J. B., arXiv:0906.2425v1 [physics.flu-dyn].Google Scholar
[7]Ladd, A. J. C., Short-time motion of colloidal particles: numerical simulation via a fluctuating lattice-Boltzmann equation, Phys. Rev. Lett., 70 (1993), 1339–1342.CrossRefGoogle Scholar
[8]Duenweg, B., Schiller, U. D., and Ladd, A. J. C., Statistical mechanics of the fluctuating lattice Boltzmann equation, Phys. Rev. E., 76 (2007), 036704.Google Scholar
[9]He, X., and Luo, L. S., A priori derivation of the lattice Boltzmann equation, Phys. Rev. E., 55 (1997), R6333–R6336.CrossRefGoogle Scholar
[10]Qian, Y. H., D. d’Humieres, and Lallemand, P., Lattice BGK models for Navier-Stokes equation, Europhys. Lett., 17 (1992), 479–484.Google Scholar
[11]d’Humieres, D., Rarefied gas dynamics: theory and simulations, Prog. Astronaut. Aeronaut., 159 (1992), 450–458.Google Scholar
[12]Lallemand, P.,and Luo, Li-Shi, Theory of the lattice Boltzmann method: dispersion, dissipation, isotropy, Galilean invariance, and stability, Phys. Rev. E., 61 (2000), 6546–6562.CrossRefGoogle ScholarPubMed
[13]Adhikari, R., and Succi, S., Duality in matrix lattice Boltzmann models, Phys. Rev. E., 78 (2008), 066701.Google Scholar
[14]Vergassola, M., Benzi, R., and Succi, S., On the hydrodynamic behaviour of the lattice Boltz-mann equation, Europhys. Lett., 13 (1990), 411–416.Google Scholar
[15]Dellar, P. J., Nonhydrodynamic modes and a priori construction of shallow water lattice Boltzmann equations, Phys. Rev. E., 65 (2002), 036309.Google Scholar
[16]Dellar, P. J., Incompressible limits of lattice Boltzmann equations using multiple relaxation times, J. Comput. Phys., 190 (2003), 351–370.Google Scholar
[17]Lifshitz, E. M., and Pitaevskii, L. P., Course of Theoretical Physics, Vol. 10, Physical Kinetics, Part 2, Pergamon Press, Oxford, 1981.Google Scholar
[18]Kaehler, G., and Wagner, A., in preparation.Google Scholar