中文摘要：

基于带化学反应的2维轴对称Euler方程,利用带有monotonized centered（MC）限制器的波传播算法,在两端敞开的圆桶中对惰性介质的聚心激波和氢气-空气混合物的聚心火焰与激波的相互作用进行了数值模拟.数值结果表明,在惰性介质中激波在轴心的每次汇聚均可成长为马赫干,马赫干的追赶使激波得到一定程度的增强,但整体还呈下降趋势.在氢气一空气混合物中,燃烧诱导的激波,由于与火焰的反复作用,使激波在轴心处产生马赫干的频率和强度皆高于惰性介质中的情形.同时,火焰在与激波的相互作用过程中发生失稳变形,使其形状呈扁平头部的蘑菇云.

英文摘要：

Based on the two-dimensional axisymmetric Euler equations coupling with chemical reactions, the phenomena of implosion wave in the inertia medium and interaction of the implosion flame with shock in the hydrogen-air mixture were numerically studied by using wave propagation algorithm with monotonized centered （MC） limiter in the cylindrical tube with two open ends. In the inertia medium the simulations show that toroidal shocks implode and reflect at the axis of symmetry of the cylindrical tube. Every implosion can form a Mach stem that propagates towards the previous Mach stems, which enhances shock but decreases in the whole because of absence of energy. In the hydrogen-air mixture the calculated results show that shock induced by combustion repeatedly interacts with implosion flame in the cylindrical tube, which leads to the fact that frequency and intensity of Mach stems at the axis of the cylindrical tube are higher than these in the inertia medium. Simultaneously, repeated shock-flame interactions cause instability and distortion of the flame, and then form the shape of collapsing flame front.