# Accession Number:

## ADA374629

# Title:

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

# Descriptive Note:

# Corporate Author:

## INSTITUTE FOR COMPUTER APPLICATIONS IN SCIENCE AND ENGINEERING HAMPTON VA

# Personal Author(s):

# Report Date:

## 2000-02-01

# Pagination or Media Count:

## 14.0

# 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.

# Descriptors:

# Subject Categories:

- Fluid Mechanics