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Finite-volume lattice Boltzmann method.

H Xi1, G Peng, S H Chou

  • 1Department of Physics and Astronomy, Bowling Green State University, Bowling Green, Ohio 43403, USA.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|April 24, 2002
PubMed
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A new finite-volume formulation for the lattice Boltzmann method (FVLBM) accurately simulates fluid dynamics. This advanced computational fluid dynamics approach extends the lattice Boltzmann method

Area of Science:

  • Computational fluid dynamics
  • Numerical analysis
  • Fluid mechanics

Background:

  • The lattice Boltzmann method (LBM) is a powerful computational fluid dynamics tool.
  • Traditional LBM implementations can face challenges with complex geometries.
  • Accurate simulation of fluid flow is crucial in various scientific and engineering fields.

Purpose of the Study:

  • To introduce a novel finite-volume formulation for the lattice Boltzmann method (FVLBM) using bilinear quadrilateral elements.
  • To validate the accuracy and flexibility of the FVLBM scheme for fluid flow simulations.
  • To extend the applicability of the lattice Boltzmann method to complex and arbitrarily shaped two-dimensional domains.

Main Methods:

  • Developed a finite-volume formulation for the lattice Boltzmann method (FVLBM) in two dimensions.

Related Experiment Videos

  • Employed standard bilinear quadrilateral elements for the spatial discretization.
  • Validated the scheme by comparing simulation results with analytical solutions of the Navier-Stokes equations for rotating Couette and Taylor vortex flows.
  • Simulated a modified rotating Couette flow with an elliptical inner cylinder.

    • Main Results:

    • The FVLBM scheme demonstrated high accuracy in simulating time-dependent rotating Couette flow and Taylor vortex flow, with results closely matching analytical Navier-Stokes solutions.
    • Simulations of a modified rotating Couette flow with an elliptical inner cylinder showed excellent agreement with results from the traditional marker-and-cell method.
    • The FVLBM scheme proved capable of handling arbitrarily shaped two-dimensional regions.

    Conclusions:

    • The developed finite-volume formulation significantly enhances the accuracy and applicability of the lattice Boltzmann method.
    • FVLBM provides a robust and flexible approach for simulating fluid dynamics in complex geometries.
    • This work extends the range of problems addressable by the lattice Boltzmann method in computational fluid dynamics.