中文摘要：

在自然界和工程物理领域存在大量的非平衡、多相等复杂系统和复杂行为。Lattice Boltzmann（LB）方法起源于复杂系统复杂行为研究的格子气或元胞自动机模型；其中，现代版的Lattice Boltzmann Kinetic Model（LBKM）植根于非平衡统计物理学的基本方程-Boltzmann方程。本文从物理学视角评述LB方法，给出单松弛因子和多松弛因子LBKM构建的统一理论，介绍其在非平衡与多相复杂系统研究方面的应用。简单列举LB在多相流、可压流、材料动理学等方面的进展，重点介绍使用LB研究流体界面不稳定性、燃烧等问题的工作。本文所重点传递的信息为：可以通过宏观量研究系统的非平衡行为、可以提供系统偏离热力学平衡引发的宏观效应是LBKM建模优越于宏观连续介质建模的地方；除了可以从更基本的层面理解相应物理系统的特征、机制和规律外，这类研究结果可以为现有程序或软件中宏观模型的改进（例如修正项的构造）提供物理参考。

英文摘要：

Nonequilibrium and multiphase complex systems are ubiquitous in natural and engineering fields. The Lattice Boltzmann （LB） method/model is originated from the lattice gas or automata model which was proposed to investigate complex behaviors in various complex systems. The current Lattice Boltzmann Kinetic Model（LBKM） is rooted in the fundamental equation of the nonequilibrium statistical physics, the Boltzmann equation. The LB model is reviewed from a physical point of view. A unified theory for the single relation time and multiple relaxation time LBKMs is presented. The modeling and simulations of various nonequilibrium and multiphase complex systems are introduced. Firstly, we briefly review the progress in modeling multiphase flows, compressible flows, soild material kinetics, etc. Then, we give more space to the progress in studying hydrodynamic interfacial instabilities, combustion phenomena, etc. It is stressed that, via the LBKM, one can probe the nonequilibrium behavior through analyzing the high-order moments which are macroscopic quantities. The LBKM can be used to investigate the macroscopic behaviors of the system due to its deviations from the thermodynamic equilibrium, which is beyond the traditional modeling based on continuum assumption. Besides the deeper physical insights into the kinetic procedures, such a methodology and observations are indicative for improving the physical models from a macroscopic level.