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Efficient kinetic method for fluid simulation beyond the Navier-Stokes equation.

Raoyang Zhang1, Xiaowen Shan, Hudong Chen

  • 1Exa Corporation, Burlington, Massachusetts 01803, USA. raoyang@exa.com

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 13, 2006
PubMed
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This study enhances the lattice Boltzmann method (LBM) for fluid dynamics simulations. The improved LBM accurately models fluid flows at various Knudsen numbers (Kn), overcoming limitations of previous models.

Area of Science:

  • Computational fluid dynamics
  • Fluid mechanics
  • Kinetic theory

Background:

  • The lattice Boltzmann method (LBM) is a kinetic-theory-based approach for simulating fluid flows.
  • Existing LBM formulations have limitations in accurately controlling the order of accuracy for nonequilibrium contributions.
  • Higher-order projections and accurate quadrature are crucial for LBM accuracy.

Purpose of the Study:

  • To present a theoretical extension of the Shan's LBM formulation.
  • To introduce a regularization procedure for consistent accuracy control.
  • To develop an LBM that accurately incorporates higher-order hydrodynamic moments.

Main Methods:

  • Theoretical extension of the kinetic-theory-based LBM.
  • Introduction of a regularization procedure for nonequilibrium contributions.

Related Experiment Videos

  • Construction of a specific LBM incorporating up to third-order hydrodynamic moments.
  • Gauss-Hermite quadrature for equilibrium distribution function projection.

    • Main Results:

    • The extended LBM overcomes defects in conventional models.
    • Accurate simulation of fluid flows at finite Knudsen numbers (Kn) is achieved.
    • Force-driven Poiseuille flow simulations predict Knudsen's minimum.
    • Asymptotic behavior of flow flux at large Kn is accurately captured.

    Conclusions:

    • The enhanced LBM provides more quantitative simulations for fluid flows with finite Kn.
    • The regularization procedure ensures consistent accuracy control in LBM.
    • The model's ability to capture Knudsen's minimum and asymptotic behavior validates its accuracy.