High-order hydrodynamics via lattice Boltzmann methods

In this work, closure of the Boltzmann-Bhatnagar-Gross-Krook (Boltzmann-BGK) moment hierarchy is accomplished via projection of the distribution function f onto a space H-N spanned by N-order Hermite polynomials. While successive order approximations retain an increasing number of leading-order moments of f, the presented procedure produces a hierarchy of (single) N-order partial-differential equations providing exact analytical description of the hydrodynamics rendered by (N-order) lattice Boltzmann-BGK (LBBGK) simulation. Numerical analysis is performed with LBBGK models and direct simulation Monte Carlo for the case of a sinusoidal shear wave (Kolmogorov flow) in a wide range of Weissenberg number Wi=tau nu k(2) (i.e., Knudsen number Kn=lambda k similar or equal to Wi(2)); k is the wave number, tau is the relaxation time of the system, and lambda similar or equal to tau c(s) is the mean-free path, where c(s) is the speed of sound. The present results elucidate the applicability of LBBGK simulation under general nonequilibrium conditions.