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Self-consistent force scheme in the spectral multiple-relaxation-time lattice Boltzmann model.

Xuhui Li1, Zuoxu Li2, Wenyang Duan1

  • 1College of ShipBuilding Engineering, Harbin Engineering University, Harbin, Heilongjiang 150001, China.

Physical Review. E
|February 17, 2024
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Summary

This study derives a new force term for the spectral multiple-relaxation-time lattice Boltzmann model. This method ensures self-consistency for isothermal and thermal flows, improving numerical simulations.

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Area of Science:

  • Computational Fluid Dynamics
  • Numerical Analysis
  • Statistical Mechanics

Background:

  • The Lattice Boltzmann Method (LBM) is a powerful numerical technique for fluid dynamics.
  • Accurate incorporation of force terms is crucial for LBM simulations, especially for complex flows.
  • Existing methods for force terms in high-order LBM can lack self-consistency.

Purpose of the Study:

  • To derive a novel force term for the spectral multiple-relaxation-time high-order lattice Boltzmann model.
  • To ensure the self-consistency of the force term in both isothermal and thermal flow simulations.
  • To provide a framework for practical numerical implementation of the derived force term.

Main Methods:

  • Expansion of the Boltzmann equation's force term in the Hermite temperature rescaled central moment (RCM) space.
  • Neglecting higher-order nonequilibrium RCM moments.
  • Incorporation of the force term within the RCM collision operator.
  • Transformation between RCM and raw moment (RM) spaces for numerical implementation.

Main Results:

  • A new force term scheme is derived for the spectral MRT high-order LBM.
  • The derived force term is demonstrated to be self-consistent for isothermal flows.
  • The scheme is also shown to be self-consistent for compressible thermal flows with adjustable Prandtl numbers.
  • Numerical experiments validate the self-consistency and applicability of the new force term.

Conclusions:

  • The developed force term scheme is a significant advancement for high-order LBM.
  • The method offers improved accuracy and reliability for simulating isothermal and thermal fluid flows.
  • This work provides a robust approach for incorporating force terms in advanced LBM.