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 HN 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=τν k2 (i.e., Knudsen number Kn=λk≃ Wi2); k is the wave number, τ is the relaxation time of the system, and λ≃τ cs is the mean-free path, where cs is the speed of sound. The present results elucidate the applicability of LBBGK simulation under general nonequilibrium conditions.