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2019 Volume 27 Issue 1
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Huanfeng Ye, Bo Kuang, Yanhua Yang. 2019: Derivation of lattice Boltzmann equation via analytical characteristic integral, Chinese Physics B, 28(1): 479-490. doi: 10.1088/1674-1056/28/1/014701
Citation: Huanfeng Ye, Bo Kuang, Yanhua Yang. 2019: Derivation of lattice Boltzmann equation via analytical characteristic integral, Chinese Physics B, 28(1): 479-490. doi: 10.1088/1674-1056/28/1/014701
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Derivation of lattice Boltzmann equation via analytical characteristic integral

  • School of Nuclear Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, China

  • School of Nuclear Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, China;National Energy Key Laboratory of Nuclear Power Software, Beijing 102209, China

  • Fund Project: the National Science and Technology Major Project, China (Grant 2017ZX06002002)
  • A lattice Boltzmann (LB) theory, the analytical characteristic integral (ACI) LB theory, is proposed in this paper. ACI LB theory takes the Bhatnagar–Gross–Krook (BGK)-Boltzmann equation as the exact kinetic equation behind Navier–Stokes continuum and momentum equations and constructs an LB equation by rigorously integrating the BGK-Boltzmann equation along characteristics. It is a general theory, supporting most existing LB equations including the standard lattice BGK (LBGK) equation inherited from lattice-gas automata, whose theoretical foundation had been questioned. ACI LB the-ory also indicates that the characteristic parameter of an LB equation is collision number, depicting the particle-interaction intensity in the time span of the LB equation, instead of the traditionally assumed relaxation time, and the over-relaxation time problem is merely a manifestation of the temporal evolution of equilibrium distribution along characteristics under high collision number, irrelevant to particle kinetics. In ACI LB theory, the temporal evolution of equilibrium distribution along characteristics is the determinant of LB method accuracy and we numerically prove this.
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    沈阳化工大学材料科学与工程学院 沈阳 110142

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Derivation of lattice Boltzmann equation via analytical characteristic integral

Abstract: A lattice Boltzmann (LB) theory, the analytical characteristic integral (ACI) LB theory, is proposed in this paper. ACI LB theory takes the Bhatnagar–Gross–Krook (BGK)-Boltzmann equation as the exact kinetic equation behind Navier–Stokes continuum and momentum equations and constructs an LB equation by rigorously integrating the BGK-Boltzmann equation along characteristics. It is a general theory, supporting most existing LB equations including the standard lattice BGK (LBGK) equation inherited from lattice-gas automata, whose theoretical foundation had been questioned. ACI LB the-ory also indicates that the characteristic parameter of an LB equation is collision number, depicting the particle-interaction intensity in the time span of the LB equation, instead of the traditionally assumed relaxation time, and the over-relaxation time problem is merely a manifestation of the temporal evolution of equilibrium distribution along characteristics under high collision number, irrelevant to particle kinetics. In ACI LB theory, the temporal evolution of equilibrium distribution along characteristics is the determinant of LB method accuracy and we numerically prove this.

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