Higher-order Galilean-invariant lattice Boltzmann model for microflows: Single-component gas

Division of Chemical and Biomolecular Engineering, School of Chemical and Biomedical Engineering, Nanyang Technological University, 637459 Singapore, Singapore.
Physical Review E (Impact Factor: 2.29). 10/2010; 82(4 Pt 2):046701. DOI: 10.1103/PhysRevE.82.046701
Source: PubMed


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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Available from: Santosh Ansumali, Apr 11, 2014
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    • "The implementation of the diffuse Maxwell boundary condition using Gauss–Laguerre off-lattice quadrature models in Ref. [41] shows good results for Couette flow up to Kn = 0.5. By using an alternative framework, a high-order LB model with only 27 discrete velocities has been developed by Yudistiawan et al. [33] and it was shown that the corresponding moment system is quite similar to Grad's 26-moment system. This off-lattice D3Q27 model is able to represent both, Knudsen layer effects and the Knudsen minimum for Poiseuille flow. "
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