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A multiple-relaxation-time collision model by Hermite expansion.

Xiaowen Shan1,2, Xuhui Li2, Yangyang Shi2

  • 1Guangdong Provincial Key Laboratory of Turbulence Research and Applications, Southern University of Science and Technology, Shenzhen 518055, People's Republic of China.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|August 30, 2021
PubMed
Summary
This summary is machine-generated.

This study introduces a new collision model for fluid dynamics simulations, improving upon the standard lattice Bhatnagar-Gross-Krook (LBGK) method. It enhances accuracy by relaxing distribution function components independently, capturing more complex fluid behaviors.

Keywords:
lattice Boltzmann equationmultiple relaxation time

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Area of Science:

  • Computational fluid dynamics
  • Mesoscale methods
  • Kinetic theory

Background:

  • The lattice Bhatnagar-Gross-Krook (LBGK) method uses a simplified collision model.
  • The standard LBGK model assumes uniform relaxation, which can be inaccurate for complex flows.
  • Existing methods lack the ability to capture certain high-order fluid dynamics phenomena.

Purpose of the Study:

  • To develop a more accurate and versatile collision model for the Boltzmann equation.
  • To improve the lattice BGK method by incorporating independent relaxation of distribution function components.
  • To accurately simulate fluid dynamics phenomena beyond the Navier-Stokes-Fourier equations.

Main Methods:

  • Formulated a new collision model based on independent relaxation of irreducible Hermite coefficient components.
  • Utilized components corresponding to the irreducible representation of the rotation group.
  • Employed the binomial transform for evaluating Hermite coefficients in the absolute frame to minimize numerical dissipation.

Main Results:

  • Identified multiple independent relaxation rates for 2nd, 3rd, and 4th moments.
  • These rates correspond to shear and bulk viscosity, thermal diffusivity, and higher-order relaxation processes.
  • Numerical verification confirmed the model's accuracy and effectiveness in reducing numerical dissipation.

Conclusions:

  • The proposed collision model offers a more refined approach than the standard LBGK method.
  • It accurately captures phenomena not described by Navier-Stokes-Fourier equations.
  • This advancement holds significant potential for mesoscale fluid dynamics simulations.