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Lattice Boltzmann Model for the Incompressible Navier–Stokes Equation

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Abstract

In this paper a lattice Boltzmann (LB) model to simulate incompressible flow is developed. The main idea is to explicitly eliminate the terms of o(M 2), where M is the Mach number, due to the density fluctuation in the existing LB models. In the proposed incompressible LB model, the pressure p instead of the mass density ρ is the independent dynamic variable. The incompressible Navier–Stokes equations are derived from the incompressible LB model via Chapman–Enskog procedure. Numerical results of simulations of the plane Poiseuille flow driven either by pressure gradient or a fixed velocity profile at entrance as well as of the 2D Womersley flow are presented. The numerical results are found to be in excellent agreement with theory.

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Authors and Affiliations

  1. Theoretical (T) Division, Los Alamos National Laboratory, Complex Systems Group (T-13), MS-B213, Los Alamos, New Mexico, 87545

    Xiaoyi He & Li-Shi Luo

  2. Los Alamos National Laboratory, Center for Nonlinear Studies (CNLS), MS-B258, Los Alamos, New Mexico, 87545

    Xiaoyi He

  3. ICASE, MS 403, NASA Langley Research Center, 6 North Dryden St., Bldg. 1298, Hampton, Virginia, 23681-0001

    Li-Shi Luo

Authors
  1. Xiaoyi He
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  2. Li-Shi Luo
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He, X., Luo, LS. Lattice Boltzmann Model for the Incompressible Navier–Stokes Equation. Journal of Statistical Physics 88, 927–944 (1997). https://doi.org/10.1023/B:JOSS.0000015179.12689.e4

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  • DOI: https://doi.org/10.1023/B:JOSS.0000015179.12689.e4

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