Thermal fluctuations in the lattice Boltzmann method for non-ideal fluids
arXiv:1009.0254 · doi:10.1103/PhysRevE.82.056714
Abstract
We introduce thermal fluctuations in the lattice Boltzmann method for non-ideal 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.
15 pages, 5 figures
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