Fluctuating ideal-gas lattice Boltzmann method with fluctuation dissipation theorem for nonvanishing velocities

Abstract

Current implementations of fluctuating ideal-gas descriptions with the lattice Boltzmann methods are based on a fluctuation dissipation theorem, which, while greatly simplifying the implementation, strictly holds only 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 multirelaxation 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 perform poorly for non vanishing mean velocity as indicated by violations of Galilean invariance of measured structure factors. Results obtained with the method introduced here show a significant reduction of the Galilean invariance violations.

Multiphase lattice Boltzmann simulations for porous media applications

“…Starting from this general approach, simplifications and extensions have led to the development of, for example, two relaxation time (TRT) models [65,66] as well as models incorporating thermal fluctuations [67][68][69][70].…”

Fluctuating multicomponent lattice Boltzmann model

“…Moreover, as emerging from Eq. (67), both the forcing and the noise need to be properly renormalized, a fact that has been already pointed out in many other papers [10,11,13,[33][34][35]. The renormalization of the forcing term is taken into account by defininḡ…”

“…The idea of including noise in LBE is also an active research field, as witnessed by the various publications of the recent years [10][11][12][13][33][34][35]. The basic idea has been pioneered by Ladd [13], who suggested the introduction of noise on the non-conserved hydrodynamic modes, thus reproducing fluctuating viscous stresses in the corresponding hydrodynamic limit (small wavevectors).…”

“…Adhikari et al [33] were the first to recognize the necessity to include noise on all the non-physical ghost modes, and Dünweg et al [34] reformulated this approach to follow a detailed-balance condition description. In a subsequent work, Kaehler & Wagner [35] also explored the fluctuating LBE for non-vanishing mean velocities. All these implementations, however, consider idealgas descriptions.…”

“…The T ai are chosen as linearly independent and orthogonal with respect to a certain norm [33][34][35]. The use of a moment space representation has the advantage that the noise can be constructed such that individual masses and total momentum are explicitly conserved.…”