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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
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Published on: December 4, 2017

Exact lattice Boltzmann equation.

F Bösch1, I V Karlin

  • 1Aerothermochemistry and Combustion Systems Lab, ETH Zurich, 8092 Zurich, Switzerland.

Physical Review Letters
|September 17, 2013
PubMed
Summary
This summary is machine-generated.

The lattice Boltzmann equation (LBE) is derived from kinetic theory without approximations. Conventional LBE simulations for hydrodynamics are disconnected from the kinetic theory domain.

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Area of Science:

  • Computational fluid dynamics
  • Kinetic theory
  • Statistical mechanics

Background:

  • The lattice Boltzmann method (LBM) is widely used for simulating fluid dynamics.
  • Existing derivations of LBM from kinetic theory rely on approximations, limiting their theoretical rigor.
  • A clear connection between LBM and fundamental kinetic theory is lacking.

Purpose of the Study:

  • To derive the lattice Boltzmann equation (LBE) rigorously from the Bhatnagar-Gross-Krook (BGK) kinetic equation.
  • To investigate the relationship between LBE and kinetic theory without relaxation approximations.
  • To determine the domain of validity for conventional LBM simulations in relation to kinetic theory.

Main Methods:

  • Derivation of the LBE using the Euler-Maclaurin integration formula.
  • Analysis of the resulting LBE and its connection to the BGK kinetic equation.
  • Comparison of the derived LBE with conventional LBM formulations.

Main Results:

  • A novel derivation of the LBE from the BGK equation is presented, free of relaxation-type approximations.
  • The derivation reveals that conventional LBM simulations operate in a parameter domain distinct from kinetic theory.
  • This finding highlights a theoretical disconnect in current LBM applications for hydrodynamics.

Conclusions:

  • The rigorous derivation provides a new theoretical foundation for the lattice Boltzmann method.
  • Conventional LBM simulations for hydrodynamics may not accurately represent the underlying kinetic theory in certain parameter regimes.
  • Further research is needed to bridge the gap between LBM and kinetic theory for broader applicability.