瞬态传热问题的微分求积和精细积分求解方法

Application of differential quadrature and precise integration methods in analysis of transient heat transfer

给出了瞬态传热问题的高效高精度求解方法,该方法分别用微分求积法(DQM)和精细积分法(PIM)离散空间域和时间域.微分求积方法除了精度高、效率高之外,处理复杂边界条件的灵活性也优于有限元法(FEM).用精细积分法处理一阶瞬态传热微分控制方程,不需要增加额外自由度,还可以达到计算机精度.给出了隔热结构4种边界条件下的数值结果.并就上表面恒温、其他面绝热边界条件计算结果与有限元分析结果进行了对比,算例分析表明,采用微分求积和精细积分法布置少量的节点就可以达到较高的精度.

An accurate and efficient solution method of the governing equation of transient heat transfer was proposed based on the differential quadrature method （DQM） and precise integration method （PIM）. DQM was applied to discretize spatial domain while PIM to temporal domain. It has been shown that DQM, with high accuracy and efficiency, also had higher flexibility than the finite element method （FEM） while dealing with complicated boundary conditions. The transient heat transfer is governed by the first-order differential equation with respect to time, while applying precise integration method in temporal domain, the same accuracy as computer can be achieved without increasing additional degrees of freedom. Numerical results were given for four kinds of boundary conditions of thermal protection structure. Then, the numerical result of the structure with constant temperature on top surface and heat insulation on other surfaces was compared with the result using the FEM. The numerical examples analysis shows that the higher precision can be achieved with fewer nodes by DQM and PIM.