Commun. Comput. Phys., 9 (2011), pp. 1315-1322.

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

Goetz Kaehler 1*, Alexander Wagner 1

1 Department of Physics, North Dakota State University, Fargo, ND 58108, USA.

Received 15 November 2009; Accepted (in revised version) 16 November 2010
Available online 18 February 2011


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.

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PACS: 47.11.-j, 47.11.Qr, 05.40.-a
Key words: Lattice Boltzmann, fluctuations, Galilean invariance.

*Corresponding author.
Email: (G. Kaehler), (A. Wagner)

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