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  • Title: Higher-order Galilean-invariant lattice Boltzmann model for microflows: single-component gas.
    Author: Yudistiawan WP, Kwak SK, Patil DV, Ansumali S.
    Journal: Phys Rev E Stat Nonlin Soft Matter Phys; 2010 Oct; 82(4 Pt 2):046701. PubMed ID: 21230406.
    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.
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