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Higher-order dynamics in lattice-based models using the chapman-enskog method

Qian1, Zhou

  • 1Department of Applied Physics and Applied Mathematics, Columbia University, New York, New York 10027, USA.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|October 25, 2000
PubMed
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This study identifies two key conditions for higher-order dynamics in lattice models using Chapman-Enskog expansion. These factors, conserved quantities and discretization, are crucial for deriving Burnett-like equations.

Area of Science:

  • Computational physics
  • Mathematical modeling

Background:

  • Lattice-based models are crucial for simulating complex physical phenomena.
  • Understanding higher-order dynamics is essential for accurate macroscopic descriptions.

Purpose of the Study:

  • Investigate the conditions for higher-order dynamics in lattice models.
  • Determine when Burnett-like equations arise from Chapman-Enskog expansion.

Main Methods:

  • Analysis of lattice-based models.
  • Application of Chapman-Enskog expansion.
  • Examination of conserved quantities and discretization schemes.

Main Results:

  • Identified two critical conditions for higher-order dynamics.
  • Demonstrated conditions using diffusion and hydrodynamic equations.

Related Experiment Videos

  • Highlighted the importance of careful derivation for lattice hydrodynamics.

    • Conclusions:

    • The number of conserved quantities and discretization significantly influence higher-order dynamics.
    • Deriving Burnett-like equations in lattice models requires specific considerations.