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Preconditioned lattice-Boltzmann method for steady flows.

Zhaoli Guo1, T S Zhao, Yong Shi

  • 1Department of Mechanical Engineering, The Hong Kong University of Science and Technology, Kowloon, Hong Kong.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 9, 2005
PubMed
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A new preconditioned lattice Boltzmann (LB) method accelerates convergence for steady incompressible flows. This enhanced LB model improves solution accuracy while retaining the benefits of standard LB methods.

Area of Science:

  • Computational fluid dynamics
  • Numerical analysis

Background:

  • Standard lattice Boltzmann (LB) methods are widely used for fluid flow simulations.
  • Steady incompressible flows present challenges in achieving rapid and accurate numerical solutions.
  • Existing LB models may have limitations in convergence speed and solution accuracy for certain flow regimes.

Purpose of the Study:

  • To introduce a preconditioned lattice Boltzmann (LB) method for steady incompressible flows.
  • To enhance the eigenvalue system of the LB model for improved performance.
  • To investigate the model's stability and compare its convergence and accuracy against the standard LB method.

Main Methods:

  • Development of a preconditioned lattice Boltzmann (LB) model.
  • Derivation of macroscopic equations and comparison with standard LB models.

Related Experiment Videos

  • Linear stability analysis for low Mach number flows.
  • Numerical testing to evaluate convergence rate and solution accuracy.

    • Main Results:

    • The proposed LB model yields macroscopic equations equivalent to standard LB models but with an improved eigenvalue system.
    • Linear stability analysis indicates stability comparable to standard LB models at low Mach numbers.
    • Numerical tests demonstrate convergence rate enhancement up to an order of magnitude.
    • Improved accuracy of the obtained flow solutions compared to the standard LB method.

    Conclusions:

    • The preconditioned LB method offers significant improvements in convergence and accuracy for steady incompressible flows.
    • The model maintains the advantageous structural properties of the standard LB method.
    • This approach provides an effective explicit solver for preconditioned compressible Navier-Stokes equations.