A precise integration boundary element method for solving transient heat conduction problems
A precise integration boundary element method for solving transient heat conduction problems
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DOI：
10.1016/j.ijheatmasstransfer.2014.07.029
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发表时间：
2014-11
影响因子：
5.2
通讯作者：
W. Yao;Bo Yu;Xiaowei Gao;Q. Gao
中科院分区：
文献类型：
--
作者：
W. Yao;Bo Yu;Xiaowei Gao;Q. Gao
本文提出了一种边界单元法和精细积分法相结合的方法来求解有热源的暂态热传导问题。利用拉普拉斯方程的格林函数推导出边界积分方程解，由此导出的积分方程组中包含两个区域积分。首先利用径向积分法将区域积分转化为等价的边界积分，从而利用边界元方法得到边界积分方程组上的常微分方程组。然后，采用精细积分法求解常微分方程组。最后，给出了几个数值算例，验证了该方法的有效性。结果表明，即使在很大的时间步长下，该方法也能获得令人满意的结果，并且如果某些积分涉及边界条件，且热源可以解析积分，则该方法的结果与时间步长无关。
In this paper, a combined approach of boundary element method and precise integration method is presented for solving transient heat conduction problems with heat sources. The boundary integral equation is derived by means of the Green’s function for the Laplace equation, and as a result, two domain integrals are involved in the derived integral equations. Firstly, the radial integration method is used to convert the domain integrals into equivalent boundary integrals, so the system of ordinary differential equations on the boundary integral equation can be obtained by the boundary element method. Then, the precise integration method is adopted to solve the system of ordinary differential equations. Finally, several numerical examples are given to demonstrate the performance of the present method. The results show that the present approach gives satisfactory performance even for very large time step size, and the results given by the present approach are independent of the time step size if some integrals involves boundary conditions and heat sources can be integrated analytically.