title: Higher-order Galilean-invariant lattice Boltzmann model for microflows: single-component gas.
abstract: We introduce a scheme which gives rise to additional degree of freedom for the same number of discrete velocities in the context of the lattice Boltzmann model. We show that an off-lattice D3Q27 model exists with correct equilibrium to recover Galilean-invariant form of Navier-Stokes equation (without any cubic error). In the first part of this work, we show that the present model can capture two important features of the microflow in a single component gas: Knudsen boundary layer and Knudsen Paradox. Finally, we present numerical results corresponding to Couette flow for two representative Knudsen numbers. We show that the off-lattice D3Q27 model exhibits better accuracy as compared to more widely used on-lattice D3Q19 or D3Q27 model. Finally, our construction of discrete velocity model shows that there is no contradiction between entropic construction and quadrature-based procedure for the construction of the lattice Boltzmann model.
authors.affiliation: Division of Chemical and Biomolecular Engineering, School of Chemical and Biomedical Engineering, Nanyang Technological University, 637459 Singapore, Singapore.
authors.forename: Wahyu Perdana
authors.initials: WP
authors.lastname: Yudistiawan
authors.forename: Sang Kyu
authors.initials: SK
authors.lastname: Kwak
authors.forename: D V
authors.initials: DV
authors.lastname: Patil
authors.forename: Santosh
authors.initials: S
authors.lastname: Ansumali