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Multiple-relaxation-time lattice Boltzmann models in three dimensions.

Dominique D'Humières1, Irina Ginzburg, Manfred Krafczyk

  • 1Laboratoire de Physique Statistique, Ecole Normale Supérieure, Paris, France. dominique.dHumieres@lps.ens.fr

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|October 11, 2005
PubMed
Summary

The multiple-relaxation-time lattice Boltzmann equation shows better numerical stability than the lattice Bhatnagar-Gross-Krook method. This study simulates 3D cavity flow using 15- and 19-velocity models.

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Area of Science:

  • Computational fluid dynamics
  • Numerical analysis
  • Statistical mechanics

Background:

  • The lattice Boltzmann equation (LBE) is a powerful computational fluid dynamics tool.
  • The lattice Bhatnagar-Gross-Krook (LBGK) model is a widely used LBE approach.
  • Limited numerical stability can be a challenge for LBGK models in certain simulations.

Purpose of the Study:

  • To present the multiple-relaxation-time lattice Boltzmann equation (MRT-LBE).
  • To demonstrate the application of MRT-LBE with 15- and 19-velocity models in 3D.
  • To compare the numerical stability of MRT-LBE against LBGK.

Main Methods:

  • Development and exposition of the multiple-relaxation-time lattice Boltzmann equation.
  • Implementation of 15-velocity and 19-velocity MRT-LBE models in three dimensions.

Related Experiment Videos

  • Simulation of diagonally lid-driven cavity flow at Reynolds numbers 500 and 2000.

    • Main Results:

    • Successful simulation of 3D diagonally lid-driven cavity flow using MRT-LBE.
    • Demonstration of enhanced numerical stability for MRT-LBE compared to LBGK.
    • Validation of the 15- and 19-velocity models for cavity flow.

    Conclusions:

    • The multiple-relaxation-time lattice Boltzmann equation offers superior numerical stability.
    • MRT-LBE is a viable and robust alternative to LBGK for complex fluid flow simulations.
    • The presented 3D models are effective for simulating lid-driven cavity flows.