We have published a number of papers on the lattice-Boltzmann method, primarily directed towards simulating particle-fluid suspensions. The most important of our earlier papers are Refs. [55,56,74,82].
A new boundary condition for a solid-fluid interface has been developed, based on the ideas of Bouzidi et al. [2], who introduced a simple and accurate interpolation scheme to account for interface locations that do not fit precisely with the lattice-Boltzmann grid. We have modified their idea by interpolating only the equilibrium part of the velocity distribution. This enables us to use information from the boundary itself to reduce the span of fluid nodes needed for the interpolation, while at the same time eliminating the viscosity dependence of the boundary location [3].
A code for simulating the dynamics of particle suspensions, Susp3D-v3.6.1, is available on request under the GPL license.
The lattice-Boltzmann model can also include thermal fluctuations in the fluid, as first described in Ref. [54]. We have recently obtained a new derivation of the fluctuating lattice Boltzmann equation [4], which is consistent with both equilibrium statististical mechanics and fluctuating hydrodynamics. The formalism is based on a generalized lattice-gas model, with each velocity direction occupied by many particles. We have shown that the most probable state of this model corresponds to the usual equilibrium distribution of the lattice Boltzmann equation. Thermal fluctuations about this equilibrium are controlled by the mean number of particles at a lattice site; a small number of particles leads to large fluctuations, while the usual deterministic lattice-Boltzman model is obtained in the limit of a very large number of particles. Stochastic collision rules are described by a Monte Carlo process satisfying detailed balance, which allows for a straightforward derivation of discrete Langevin equations for the fluctuating modes. It is shown that all non-conserved modes should be thermalized, as first pointed out by Adhikari