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Consistent forcing scheme in the cascaded lattice Boltzmann method.

Linlin Fei1, Kai Hong Luo1,2

  • 1Center for Combustion Energy, Key laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Thermal Engineering, Tsinghua University, Beijing 100084, China.

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|January 20, 2018
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Summary
This summary is machine-generated.

This study introduces a consistent forcing scheme for the cascaded lattice Boltzmann method (CLBM) within a multiple-relaxation-time (MRT) framework. Numerical simulations confirm its accuracy and isotropy, clarifying the relationship between MRT LBM and CLBM.

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Area of Science:

  • Computational Fluid Dynamics
  • Numerical Methods
  • Fluid Mechanics

Background:

  • The cascaded lattice Boltzmann method (CLBM) is an extension of the lattice Boltzmann method (LBM) used for fluid flow simulations.
  • Existing forcing schemes for CLBM have limitations in consistency and accuracy.
  • Understanding the relationship between different LBM frameworks is crucial for developing robust numerical methods.

Purpose of the Study:

  • To derive an alternative formulation of the CLBM within a general multiple-relaxation-time (MRT) framework.
  • To develop and analyze a consistent forcing scheme for the CLBM.
  • To clarify the relationship between the MRT LBM and CLBM.

Main Methods:

  • Introduction of a shift matrix to unify CLBM and MRT LBM.
  • Development of a consistent forcing scheme based on the unified framework.
  • Numerical simulations of canonical fluid dynamics problems to validate the scheme.

Main Results:

  • The CLBM is shown to be a special case of the general MRT framework when the shift matrix is a unit matrix.
  • The developed consistent forcing scheme demonstrates second-order spatial convergence and isotropy.
  • Numerical results validate the consistency of the nonslip boundary condition implementation.

Conclusions:

  • A unified framework for CLBM and MRT LBM is established using a shift matrix.
  • The proposed consistent forcing scheme offers improved accuracy and physical properties for CLBM simulations.
  • This work provides a clearer understanding of the theoretical connections between different LBM variants.