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Lattice Boltzmann method for the compressible Euler equations.

Takeshi Kataoka1, Michihisa Tsutahara

  • 1Graduate School of Science and Technology, Kobe University, Rokkodai, Nada, Kobe 657-8501, Japan. kataoka@mech.kobe-u.ac.jp

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|July 13, 2004
PubMed
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A new lattice Boltzmann model for compressible Euler equations is introduced, accurately simulating flows with shock waves. This model overcomes previous limitations, providing a robust theoretical foundation for complex fluid dynamics.

Area of Science:

  • Computational fluid dynamics
  • Fluid mechanics
  • Numerical analysis

Background:

  • Lattice Boltzmann methods (LBM) are widely used for fluid simulations.
  • Existing LBM for compressible Euler equations have limitations, particularly with free choice of specific-heat ratio.
  • Simulating flows with shock waves and discontinuities remains a challenge for LBM.

Purpose of the Study:

  • To propose a novel lattice Boltzmann model for the compressible Euler equations.
  • To provide a rigorous theoretical foundation for the model, addressing limitations of previous approaches.
  • To enable accurate simulation of fluid flows, including those with shock waves and contact discontinuities.

Main Methods:

  • Development of a lattice Boltzmann model for compressible Euler equations.

Related Experiment Videos

  • Rigorous theoretical derivation of macroscopic variable behavior in different solution variation regimes.
  • Analysis of the model's behavior in the limit of small Knudsen numbers.
  • Inclusion of shock waves and contact discontinuities in the theoretical framework.

    • Main Results:

    • The proposed model overcomes the limitation of a fixed specific-heat ratio.
    • Macroscopic variables satisfy compressible Euler equations for moderate solution variations (no shocks/discontinuities).
    • Macroscopic variables satisfy the weak form of Euler equations for steep variations (shocks/discontinuities).
    • Theoretical foundation established for LBM simulating flows with shock waves and discontinuities.

    Conclusions:

    • The novel lattice Boltzmann model provides a theoretically sound framework for compressible Euler equations.
    • The model accurately captures fluid behavior across different variation regimes, including shock waves.
    • This work lays the foundation for advanced LBM applications in complex fluid dynamics simulations.