压差方程Chapman-Jouguet燃烧模型爆轰波与激波的相互作用  

Interaction of detonation waves with shock waves of pressure-gradient equations for Chapman-Jouguet combustion model

作　　者：林佳青 赖耕[1] 盛万成[1] 

机构地区：[1]上海大学理学院,上海200444

出　　处：《应用数学与计算数学学报》2017年第1期96-106,共11页Communication on Applied Mathematics and Computation

基　　金：国家自然科学基金资助项目(11371240;11301326);上海市教委资助项目(13ZR1454100;11ZZ84)

摘　　要：研究了气体动力学压差方程Chapman-Jouguet(CJ)燃烧模型爆轰波与激波的相互作用.给出了该CJ燃烧模型的几类基本波线:激波线、疏散波线、强爆轰波线和CJ爆轰波线.通过研究该CJ燃烧模型的初值为三片常状态的一类初值问题,并利用相平面分析的方法构造出该问题的整体分片光滑解,得到了压差方程CJ燃烧模型爆轰波与激波相互作用的结果.进一步地,得到了对应燃烧Riemann问题解的初值扰动稳定性.The interactions of detonation waves with shock waves of pressuregradient equations for Chapman-Jouguet （C J） combustion model are studied. The elementary wave curves including the shock wave curve, the rarefaction wave curve, the strong detonation wave curve, and the CJ detonation wave point for this CJ combustion model are given. The initial value problems for the CJ combustion model with initial data of three constant states are considered, and the global piecewise smooth solutions to these problems are constructed by the phase plane analysis method. The result of interactions of detonation waves and shock waves of pressure-gradient equations for the Chapman-Jouguet （C J） combustion model is obtained. Furthermore, the stability with small perturbation in initial data of the solutions for the corresponding Riemann problems of combustion model is gotten.

关 键 词：Chapman-Jouguet燃烧模型 压差方程 爆轰波 波的相互作用 

分 类 号：O175.2[理学—数学]