A Three-Dimensional Semiclassical Lattice Boltzmann Method for Lid-Driven Cubic Cavity Flows

Abstract

A three-dimensional lattice Boltzmann method based on the Uehling-Uhlenbeck Boltzmann-BGK equation is presented. The method is directly derived by projecting the kinetic governing equation onto the tensor Hermite polynomials and various hydrodynamic approximation orders can be achieved. The intrinsic discrete nodes of the three-dimensional Gauss-Hermite quadrature provide the natural lattice velocities for the semiclassical lattice Boltzmann method. Simulations of the lid-driven cubic cavity flows based on D3Q19 lattice model for several Reynolds numbers and different particle statistics are shown to illustrate the method. The results indicate distinct characteristics of the effects of quantum statistics.