报告题目：The Lattice Boltzmann Equation:What Do We Know and What Can We Do with It?

报告人：Prof. Li-Shi Luo(罗礼诗 教授) Old Dominion Univeristy, USA

报告时间：12月13日10:30—11:30pm（周三上午）

报告地点：清华大学高等研究中心地下报告厅

主办研究所：清华大学周培源应用数学研究中心

摘要：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) flow through porous media and free-surface flows. 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 to be dealt with by particle methods (e.g., DSMC or molecular dynamics), and it can be applicable to bio- and nano-fluid systems.

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