发汗控制方程的数学求解  

MATHEMATICAL SOLUTION OF TRANSPIRATION CONTROL EQUATION

作　　者：高伟[1] 杨学实[1] 

机构地区：[1]航空航天部二院,北京100854

出　　处：《计算物理》1991年第2期165-173,共9页Chinese Journal of Computational Physics

摘　　要：本文研究了发汗控制方程的求解问题,发现在一定条件下,采用变量替换,能够将其归入古典热传导方程一类,从而得到了解析解。在计算机上对该解析式进行数值计算,证实了解的存在、唯一和稳定性。初步探明了该类控制系统在工程应用中的理论问题。该类方程的差分数值计算表明,当差分步长变小时,差分解很快逼近解析解。由于差分格式所限,存在R·BT=βτ/4h力关系,使得稳定的数值解限制在R及BT轴与上述关系曲线围成的区域内。再次证实了文献[2]的主要结论。A solution of transpiration control equation is investigated in this paper. It is found that the equation can be classified as the classic heat transfer equation under certain conditions by means of variable alternation and then the analytic solution can be obtained. A numerical calculation of the analytic solution by a computer has proved the existence, uniqueness and stability of the solution. The theoretical problem of this sort of control system applied in the engneering is preliminarily ascertained. A finite difference numerical calculation has shown that the smaller the difference step is, the faster the difference solution approaches the analytic one. Because of limitation of the difference method, the steady numerical solution can be gotten in the region surrounded by R =0 , BT = 0 and R .BT =B/ 4h . The main conclusion of reference [2] is verified again.

关 键 词：发汗 数学分析 热传导 炮弹 

分 类 号：TJ410.2[兵器科学与技术—火炮、自动武器与弹药工程]