Microflow Simulations via the Lattice Boltzmann Method

Abstract

The exact solution to the hierarchy of nonlinear lattice Boltzmann kinetic equations, for the stationary planar Couette flow for any Knudsen number was presented by S. Ansumali et al. [Phys. Rev. Lett., 98 (2007), 124502]. In this paper, simulation results at a non-vanishing value of the Knudsen number are compared with the closed-form solutions for the higher-order moments. The order of convergence to the exact solution is also studied. The lattice Boltzmann simulations are in excellent agreement with the exact solution.