中文摘要：

燃烧系统的诸多模拟依托于流体建模,离散Boltzmann方法（discrete Boltzmann method,DBM）是近年来发展起来的一种新的流体介观建模方法.本文简要评述DBM发展的两个方向——Navier-Stokes等偏微分方程的数值逼近解法和复杂系统的微介观动理学建模.主要介绍在燃烧系统模拟方面DBM已有的工作、新近的思路、与传统流体建模的异同以及近期的研究成果.本文重点传递的信息为：作为复杂系统微介观动理学建模出现的DBM在模拟过程中同时给出＂流动＂及其相伴随的、关系最密切的那部分＂热动＂非平衡效应;它为燃烧等复杂系统中各类非平衡行为的描述、非平衡信息的提取、非平衡程度的度量提供了一种简洁、有效的方法;它所提供的热动非平衡测量量有两类：一类是直接比较分布函数和平衡态分布函数的动理学矩关系得到的,一类是来自于Chapman-Enskog多尺度分析给出的热传导和黏性项.基于第二类DBM,可以实现（燃烧等）一大类复杂流体系统的多尺度物理建模.

英文摘要：

Detonation is a kind of self-propagating supersonic combustion where the chemical reaction is rapid and violent under an extreme condition.The leading part of a detonation front is pre-shocked by a strong shock wave propagating into the explosive and triggering chemical reaction.The combustion system can be regarded as a kind of chemical reactive flow system.Therefore,the fluid modeling plays an important role in the studies on combustion and detonation phenomena.The discrete Boltzmann method（DBM） is a kind of new fluid modeling having quickly developed in recent thirty years.In this paper we review the progress of discrete Boltzmann modeling and simulation of combustion phenomena.Roughly speaking,the discrete Boltzmann models can be further classified into two categories.In the first category the DBM is regarded as a kind of new scheme to numerically solve partial differential equations,such as the Navier-Stokes equations,etc.In the second category the DBM works as a kind of novel mesoscopic and coarse-grained kinetic model for complex fluids.The second kind of DBM aims to probe the trans- and supercritical fluid behaviors or to study simultaneously the hydrodynamic non-equilibrium（HNE） and thermodynamic non-equilibrium（TNE） behaviors.It has brought significant new physical insights into the systems and promoted the development of new methods in the fields.For example,new observations on fine structures of shock and detonation waves have been obtained;The intensity of TNE has been used as a physical criterion to discriminate the two stages,spinodal decomposition and domain growth,in phase separation;Based on the feature of TNE,some new front-tracking schemes have been designed.Since the goals are different,the criteria used to formulate the two kinds of models are significantly different,even though there may be considerable overlaps between them.Correspondingly,works in discrete Boltzmann modeling and simulation of combustion systems can also be classified into two categories in terms of the two kin