Runge-Kutta法在瞬态温度场的应用

Application of Runge-Kutta method in the transient temperature field

对瞬态温度场求解常用差分法,但差分法会随着迭代过程而出现震荡,精度下降,效率不高,而Runge-Kutta法是一种特殊的单步法,精度高,效率高,广泛应用于求解常微分问题。用MATLAB对瞬态温度场分布问题求解的Crank-Nicholson法和Runge-Kutta法进行编程及实现,通过结果对比发现,Runge-Kutta法的计算精度不仅比CrankNicholson法高,且模拟效率也较后者的有显著提高,其中模拟效率提高幅度最大,达到35%。

The difference method is commonly used to solve transient temperature field,but the difference method will oscillate with the iteration process,the accuracy will decrease,and the efficiency is not high.Runge-Kutta method is a special one-step method with high accuracy and efficiency,which is widely used to solve ordinary differential problems.In this paper,the rank-Nicholson method and Runge-Kutta method for solving the transient temperature field distribution problem are programmed and realized by using MATLAB.By comparing the results,it is found that the calculation accuracy of Runge-Kutta method is not only higher than Crank-Nicholson method,but also the simulation efficiency is significantly higher than that of Crank-Nicholson method.Among them,the simulation efficiency is improved by the largest margin,reaching 35%.