Kinetic theory-based force analysis in lattice Boltzmann equation

Lin Zheng, Song Zheng () and Qinglan Zhai ()
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Lin Zheng: MIIT Key Laboratory of Thermal Control of Electronic Equipment, School of Energy and Power Engineering, Nanjing University of Science and Technology, Nanjing 210094, P. R. China
Song Zheng: School of Mathematics and Statistics, Zhejiang University of Finance and Economics, Hangzhou 310018, P. R. China
Qinglan Zhai: School of Economics Management and Law, Chaohu University, Chaohu 238000, P. R. China

International Journal of Modern Physics C (IJMPC), 2019, vol. 30, issue 04, 1-10

Abstract: In the gas kinetic theory, it is shown that the zeroth order of the density distribution function f(0) and local equilibrium density distribution function were the Maxwellian distribution f(eq)(ρ,u,T) with an external force term, where ρ is the fluid density, u is the physical velocity and T is the temperature, while in the lattice Boltzmann equation (LBE) method, numerous force treatments were proposed with a discrete density distribution function fi apparently relaxed to a given state fi(eq)(ρ,u∗), where the given velocity u∗ could be different with u, and the Chapman–Enskog (CE) analysis showed that fi(0) and local equilibrium density distribution function should be fi(eq)(ρ,u∗) in the literature. In this paper, we start from the kinetic theory and show that the fi(0) and local equilibrium density distribution function in LBE should obey the Maxwellian distribution fi(eq)(ρ,u) with fi relaxed to fi(eq)(ρ,u∗), which are consistent with kinetic theory. Then the general requirements for the force term are derived, by which the correct hydrodynamic equations could be recovered at Navier–Stokes (NS) level, and numerical results confirm our theoretical analysis.

Keywords: Lattice Boltzmann; force analysis; kinetic theory (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1142/S0129183119500220

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