High-Order Hydrodynamics from Boltzmann-BGK

2009/09/06 by Colosqui, Carlos E.
#FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn)

paper · doi:10.48550/arxiv.0909.1004

Abstract

In this work, closure of the 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 (LBGK) simulation. Numerical analysis is performed with LBGK models and direct simulation Monte Carlo (DSMC) for the case of a sinusoidal shear wave (Kolmogorov flow) in a wide range of Weissenberg number Wi=τνk² (i.e. Knudsen number Kn=λk=√(Wi)); k is the wavenumber, τ the relaxation time of the system, λ≃τc_s the mean-free path, and c_s the speed of sound. The present results elucidate the applicability of LBGK simulation under general non-equilibrium conditions.

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