Some Recent Results on Discrete Velocity Model and Ramifications for Lattice Boltzmann Equation

Abstract

Some rigorous results on discrete velocity models are briefly reviewed and their ramifications for the lattice Boltzmann equation (LBE) are discussed. In particular, issues related to thermodynamics and H-theorem of the lattice Boltzmann equation are addressed. It is argued that for the lattice Boltzmann equation satisfying the correct hydrodynamic equations, there cannot exist an H-theorem. Nevertheless, the equilibrium distribution function of the lattice Boltzmann equation can closely approximate the genuine equilibrium which minimizes the H-function of the corresponding continuous Boltzmann equation. It is also pointed out that the equilibrium in the LBE models is an attractor rather than a true equilibrium in the rigorous sense of H-theorem. Since there is no H-theorem to guarantee the stability of the LBE models at the attractor, the stability of the attractor can only be studied by means other than proving an H-function.

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 2000
Accession Number
ADA374629

Entities

People

  • Li-shi Luo

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Automata
  • Boltzmann Equation
  • Consistency
  • Crystal Lattices
  • Distribution Functions
  • Dynamics
  • Engineering
  • Equations
  • Equations Of State
  • Fluid Dynamics
  • Fluid Flow
  • Hydrodynamics
  • Kinetic Theory
  • Mach Number
  • Models
  • Thermodynamic Properties
  • Thermodynamics

Fields of Study

  • Mathematics

Readers

  • Fluid Dynamics.
  • Linear Algebra
  • Plasma Physics / Magnetohydrodynamics