瞬态温度场灵敏度分析的精细积分法

SENSITIVITY ANALYSIS OF TRANSIENT HEAT CONDUCTION WITH PRECISE TIME INTEGRATION METHOD

结合有限元法 ,提出了线性和非线性瞬态温度场灵敏度分析的精细积分方法。在精细积分法求解线性和非线性温度场的基础上 ,采用敏度分析的半解析法 ,推导了瞬态温度场灵敏度分析的精细积分列式。指出对于线性热传导问题 ,精细积分法求解敏度方程同样具有稳定、高精度的数值特性 ,而且能避免常规差分法的数值振荡现象。对于非线性热传导问题 ,提出了相应的求解办法。

Sensitivity analysis of transient heat conduction is very important for thermal optimization and inverse heat conduction problem. In this paper, Precise Time Integration(PTI) method is introduced to solve the sensitivity equations of transient heat conduction in conjunction with finite element method and semi analytical method. PTI method is a very special time integration scheme. It is explicit stable and has very high precision. Furthermore, this scheme is apt to cover the stiff problem of ordinary differential equations. So this algorithm is drawing more and more attentions. In the research, detailed formulations of PTI are proposed for linear and nonlinear heat conduction. Temperature dependent conductivity and radiation boundary condition are taken into account. Predictor corrector method is employed to solve the nonlinear equations. Thereafter the methods are extended to sensitivity analysis. The procedures of thermal analysis and sensitivity analysis are very similar, so it is easy to implement the algorithm. Numerical examples showed that, as for linear problem PTI not only can give very high precise numerical results but also can avoid the numerical oscillation which often appear in conventional time difference methods; as for nonlinear problem, PTI can also give good results. PTI is an appropriate algorithm for sensitivity analysis of transient heat conduction.