Fluctuating ideal-gas lattice Boltzmann method with fluctuation dissipation theorem for nonvanishing velocities
G. Kaehler and A. J. Wagner
Accepted
Current implementations of fluctuating ideal gas discriptions with the lattice Boltzmann methods are based on a fluctuation dissipation theorem, which, while greatly simplifying the implementation, strictly only holds for zero mean velocity and small fluctuations. We show how to derive the fluctuation dissipation theorem for all k which was done only for k = 0 in previous derivations. The consistent derivation requires, in principle, locally velocity dependent multi-relaxation time transforms. Such an implementation is computationally prohibitively expensive but, with a small computational trick, it is feasible to reproduce the correct FDT without overhead in computation time. It is then shown that the previous standard implementations break down for non vanishing mean velocity as indicated by violations of Galilean invariance of measured structure factors whereas the new method performs significantly better.