THURSDAY, April 8, 2004
Time: 3:00 - 4:00 PM
Constant Hall Room 1008

Dr. Li-Shi Luo
Research Fellow
National Institute of Aerospace
Hampton, VA

In this presentation I shall first provide a brief review on what we know about the lattice Boltzmann equation, i.e., the mathematical theory behind the lattice Boltzmann equation (LBE). It can be demonstrated that the lattice Boltzmann equation is a "coherent" finite-difference equation derived from linearized Boltzmann equation. (The phrase "coherent" is used to describe the coupled discretization of phase space and time.) The lattice Boltzmann equation can also be shown as a system of moments on discrete lattice space with discrete time. In the diffusive limit, one can show that the LBE system simulate the incompressible Navier-Stokes equations. The second part of my presentation I shall attempt to show the audience about what we can do with the LBE method. I shall demonstrate a few examples: (1) direct numerical simulations (DNS) of isotropic turbulence and large-eddy simulations by the LBE method; (2) suspensions in fluids; and (3) multi-component flow through porous media. Through these examples I shall discuss pros and cons of the LBE method. More importantly, we hope to show that the lattice Boltzmann equation, as a mesoscopic method, could be an effective means to smoothly extend continuum/macroscopic methods (e.g., Navier-Stokes equations) into non-continuum regions which have be be dealt with by particle methods (e.g., DSMC or molecular dynamics).