Fluctuating Lattice Boltzmann

Fluctuations are important for many hydrodynamic phenomena such as colloid diffusion or phase-separation near the critical point. However, the standard LB-schemes do not take fluctuations into account. Based on Ladd's [1] and later Adhikari's [2] work we explain how one can practically implement noise in Lattice Boltzmann algorithms for different dimensionality and base velocity sets. We also present a new velocity moment method for deriving the hydrodynamic equations from the underlying Multi Relaxation Time models [3,4]. This sets the foundation for formulating more general fluctuating lattice Boltzmann methods for energy conserving thermal systems and multi-component systems.\\[4pt] [1] A.J.C.~Ladd, Phys. Rev. Lett {\bf70}, 1339 (1993)\\[0pt] [2] R.~Adhikari, K.~Stratford, M.E.~Cates and A.J.~Wagner, Europhys. Lett. {\bf71}, 473 (2005)\\[0pt] [3] D.~d'Humieres, in {\it Rarefied Gas Dynamics: Theory and Simulations, Prog. Astronaut. Aeronaut} {\bf159} 450 (1992)\\[0pt] [4] R.~Benzi, S.~Succi, and M.~Vergassola, Physics Reports {\bf222}, 145 (1992)