Yudistiawan Wahyu P, Ansumali Santosh, Karlin Iliya V
School of Chemical and Biomedical Engineering, Nanyang Technological University, 639798 Singapore.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Jul;78(1 Pt 2):016705. doi: 10.1103/PhysRevE.78.016705. Epub 2008 Jul 24.
Recently, analytical solutions for the nonlinear Couette flow demonstrated the relevance of the lattice Boltzmann (LB) models to hydrodynamics beyond the continuum limit [S. Ansumali, Phys. Rev. Lett. 98, 124502 (2007)]. In this paper, we present a systematic study of the simplest LB kinetic equation-the nine-bit model in two dimensions--in order to quantify it as a slip flow approximation. Details of the aforementioned analytical solution are presented, and results are extended to include a general shear- and force-driven unidirectional flow in confined geometry. Exact solutions for the velocity, as well as for pertinent higher-order moments of the distribution functions, are obtained in both Couette and Poiseuille steady-state flows for all values of rarefaction parameter (Knudsen number). Results are compared with the slip flow solution by Cercignani, and a good quantitative agreement is found for both flow situations. Thus, the standard nine-bit LB model is characterized as a valid and self-consistent slip flow model for simulations beyond the Navier-Stokes approximation.
