基于无网格边界元法的瞬态热传导问题研究

Study on Transient Heat Conduction by Meshless Boundary Element Method

对于有内热源的瞬态传热问题,由于域内积分使求解复杂化,研究了一种无需域内离散划分网格的纯边界元法。首先采用格林定理将域内积分转换成边界积分,然后利用自适应辛普森法进行插值,推导了热源依赖时间参数和不依赖时间参数两种情况的数值实现方法。最后引入不同热源情况及时间依赖性的三个数值算例进行温度分布仿真分析。仿真结果与传统的有限元解吻合良好,证明数值推导的正确性及程序调试的有效性,且该方法计算量小,使有内热源的瞬态传热分析大大简化。

The transient heat conduction problems with heat sources was studied by a boundary element method without domain discretization. Firstly, the domain integrals were transformed into boundary integrals by Green＇ s theorem, then the adaptive Simpson method was used for interpolation. The numerical implementation methods were obtained with time-dependent and time-independent. Finally three numerical examples were presented with different heat sources time dependence, and the temperature distribution simulations were showed. The method and program were deemed correct because the simulations agreed well with the classical finite element results. The analysis is simplified by this method for transient heat conduction with heat sources and the calculating amount is reduced.