Asymptotic analysis of multiple-relaxation-time lattice Boltzmann schemes for mixture modeling

AbstractA new lattice Boltzmann model for simulating ideal mixtures has been developed by means of the multiple-relaxation-time (MRT) approach. When compared with the previous single-relaxation-time (SRT) formulation of the same model, based on the continuous kinetic theory, the new model offers the possibility to independently tune the mutual diffusivity and the effects of cross collisions on the effective stress tensor. The additional degrees of freedom, due to the increased set of relaxation time constants used for modeling the cross collisions, allow us to match the experimental data on macroscopic transport coefficients. Two different integration rules, i.e. the forward Euler and the modified mid-point integration rule, were used in order to numerically integrate the developed model. Unfortunately the simpler forward Euler integration rule violates the mass conservation and there is no way to fix the problem by changing the definition of the macroscopic velocity. On the other hand, a small correction has been purposely designed for compensating this error by means of the mid-point integration rule. Some numerical simulations are reported for proving the effectiveness of the proposed corrective factor. For the considered application, the asymptotic analysis, recently suggested as an effective tool for analyzing the macroscopic equations corresponding to the lattice Boltzmann schemes, offers a remarkable advantage in comparison with the classical Chapman–Enskog technique, because it easily deals with leading terms in the distribution functions, which are no more Maxwellian

Stationary state of a heated granular gas: fate of the usual H-functional

We consider the characterization of the nonequilibrium stationary state of a randomly-driven granular gas in terms of an entropy-production based variational formulation. Enforcing spatial homogeneity, we first consider the temporal stability of the stationary state reached after a transient. In connection, two heuristic albeit physically motivated candidates for the non-equilibrium entropy production are put forward. It turns out that none of them displays an extremum for the stationary velocity distribution selected by the dynamics. Finally, the relevance of the relative Kullbach entropy is discussed.Comment: 17 pages, 2 figures, to be published in Physica