Fluctuating lattice BoltzmannR. Adhikari1, K. Stratford2, M. E. Cates1 and A. J. Wagner3
1 School of Physics, University of Edinburgh, JCMB Kings Buildings Mayfield Road, Edinburgh EH9 3JZ, UK
2 EPCC, University of Edinburgh, JCMB Kings Buildings Mayfield Road, Edinburgh EH9 3JZ, UK
3 Department of Physics, North Dakota State University - Fargo ND58105, USA
received 20 December 2004; accepted in final form 30 May 2005
published online 29 June 2005
The lattice Boltzmann algorithm efficiently simulates the Navier-Stokes equation of isothermal fluid flow, but ignores thermal fluctuations of the fluid, important in mesoscopic flows. We show how to adapt the algorithm to include noise, satisfying a fluctuation-dissipation theorem (FDT) directly at lattice level: this gives correct fluctuations for mass and momentum densities, and for stresses, at all wave vectors k. Unlike previous work, which recovers FDT only as , our algorithm offers full statistical mechanical consistency in mesoscale simulations of, e.g., fluctuating colloidal hydrodynamics.
82.70.Dd - Colloids.
24.60.-k - Statistical theory and fluctuations.
67.55.Fa - Hydrodynamics.
© EDP Sciences 2005