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Multigrid dual-time-stepping lattice Boltzmann method.

Simon Gsell1, Umberto D'Ortona1, Julien Favier1

  • 1Aix-Marseille Univ., CNRS, Centrale Marseille, M2P2, Marseille, France.

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A new dual-time-stepping lattice Boltzmann method removes time-step restrictions, enabling faster simulations and improved accuracy for fluid dynamics. This approach enhances computational efficiency and allows for filtering of unwanted pressure waves in complex flow scenarios.

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Area of Science:

  • Computational Fluid Dynamics
  • Numerical Methods

Background:

  • The lattice Boltzmann method (LBM) typically requires small time steps due to acoustic scaling, limiting simulation speed.
  • Existing LBM implementations face challenges in efficiently handling complex flow dynamics and resolving various timescales.

Purpose of the Study:

  • To develop a second-order dual-time-stepping lattice Boltzmann method (LBM) that eliminates time-step restrictions.
  • To improve the efficiency and applicability of LBM for simulating steady and unsteady laminar flows.

Main Methods:

  • Implementation of a second-order dual-time-stepping approach within the LBM framework.
  • Utilizing an external source term in the LBM equation to handle time derivatives of macroscopic quantities.
  • Employing a multigrid method to accelerate convergence of the steady-state solver.
  • Coupling a two-relaxation time model with an immersed-boundary method for flow simulation.

Main Results:

  • The dual-time-stepping LBM successfully removes time-step restrictions, allowing for adjustable physical time steps.
  • A significant speed-up (factor of 4 achieved for unsteady flow past a cylinder) is realized by increasing the time step while maintaining accuracy.
  • The method accurately reproduces unsteady laminar flows and demonstrates improved convergence rates for steady flows due to the multigrid acceleration.
  • Adjusting the time step effectively filters high-frequency pressure waves without affecting primary flow dynamics.

Conclusions:

  • The proposed dual-time-stepping LBM offers a significant advancement in computational efficiency for fluid dynamics simulations.
  • The ability to freely adjust the time step enhances simulation speed and provides a mechanism for timescale control and noise filtering.
  • This method broadens the applicability of LBM to a wider range of complex fluid flow problems.