Thermal fluctuations in the lattice Boltzmann method for nonideal fluids
M. Gross, R. Adhikari, M. E. Cates, F. Varnik.
Physical Review E, 82, 056714, (2010)
We introduce thermal fluctuations in the lattice Boltzmann method for nonideal fluids. A fluctuation-dissipation theorem is derived within the Langevin framework and applied to a specific lattice Boltzmann model that approximates the linearized fluctuating Navier-Stokes equations for fluids based on square-gradient free-energy functionals. The obtained thermal noise is shown to ensure equilibration of all degrees of freedom in a simulation to high accuracy. Furthermore, we demonstrate that satisfactory results for most practical applications of fluctuating hydrodynamics can already be achieved using thermal noise derived in the long-wavelength limit.