Modelling thermal fluctuations in non-ideal fluids with the lattice Boltzmann method
M. Gross, R. Adhikari, M. E. Cates, F. Varnik.
Philosophical Transactions of The Royal Society A, 13, 2274–2282, (2011)
Recently, we proposed a theoretical framework to include thermal ﬂuctuations into the Lattice Boltzmann (LB) method for non-ideal ﬂuids. Here, we apply a variant thereof to a certain class of force-based non-ideal ﬂuid LB models. We ﬁnd that ideal-gas-like noise is an exact result of the ﬂuctuation–dissipation theorem in the hydrodynamic regime. It is shown that satisfactory equilibration of the density and ﬂuid momentum can be obtained in a simulation over a wide range of length scales.
Keyword(s): lattice Boltzmann method; non-ideal ﬂuids; thermal noise; ﬂuctuation–dissipation theorem