脉冲化学激光简化模型的数学处理和求解

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本文给出了光引发 F_2/H_2链反应脉冲化学激光的简化模型及其 FORTRAN 程序。解决了振转跃迁光流方程与动力学速率方程之间关于时间坐标的相容性问题。按照振转跃迁光流产生与消失的准则,依时间坐标变换将脉冲化学激光简化模型问题转化为求解方程个数不同的多个常微初值问题。本模型的求解依光流产生与否划分为四个时期:(1)振转跃迁光流产生的前期。在此期间解一个只由动力学速率方程组成的常微初值问题,直至求解到某个振转跃迁光流产生时为止。(2)振转跃迁光流的消失期。在此期间,依光流出现的先后次序解一连串的常微初值问题。初值问题中光流方程的有无,取决于光流产生与否。(3)振转跃迁光流的消失期。在此期间,依光流消失的先后次序,解一连串的初值问题,直至光流方程全部退出为止。(4)振转跃迁光流消失后的结束期。此时解一个无光流方程参加的常微初值问题,直至求解到 H_2的浓度小于ε(例如ε=10~(-10))时为止。 In this paper, a simplified model of pulsed chemical laser with F 2 / H 2 chain reaction and its FORTRAN program are given. Solve the vibration transition optical flow equation and kinetic rate equation between the time coordinate compatibility. According to the criteria of the generation and disappearance of the optical transition due to the transition, the simplified model of pulsed chemical laser is transformed into several ordinary and initial values ​​with different number of equations according to time coordinate transformation. The solution of this model is divided into four periods depending on whether the optical flow is generated or not: (1) The early stage of the optical transition generated by the transition transition. In the meantime, we solve an ordinary and very initial value problem that is only composed of the kinetic rate equations, until the moment when a rotational transition optical flow is generated. (2) Vortex transition extinction period. In the meantime, according to the order of appearance of light flow, a series of ordinary and micro initial value problems are solved. The problem of the initial value of the optical flow equation, depending on whether the optical flow or not. (3) Vortex transition disappear period of optical flow. During this period, a series of initial value problems are solved according to the order of disappearance of the optical flow until all optical flow equations exit. (4) vibration transition disappear after the end of the optical flow. At this point, we solve the ordinary and micro initial value problem of a non-optical flow equation until the concentration of H 2 is less than ε (for example, ε = 10 ~ (-10)).
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