多域边界面法在稳态热传导问题中的应用

Application of Multi-domain Boundary Face Method in Steady State Heat Conduction

将边界面法应用于多域问题稳态热传导的计算,提出了一种新的实现方法,称之为多域边界面法(MD-BFM).在边界面的基础上,仿照单域问题,推导了多域问题稳态热传导的矩阵组装的方式,得出其离散的边界积分方程,温度等未知量即可求出.将多域边界面法应用于某包含62个浇筑层(共125个域)的大坝的稳态热传导分析,得出其温度场分布图,并和有限元计算结果进行了比较,温度最大值均为20.7℃,且温度分布等值线高度吻合,但多域边界面法采用了更少的网格.对大坝这样的大规模工程问题进行计算的结果证明,本文所提出的多域边界面法可以应用于稳态热传导问题,并且相较于其他方法(例如有限元法),具有同等精度,并且消耗更少的人力.

This paper presented a multi-domain boundary face method （MD-BFM） to solve steady-state heat conduction problems in large-scale engineering structures. Based on BFM, and using a similar ap- proach as that in single-domain problems, this paper derived the matrix assembly process in multi-domain problems. Then, temperature and other unknown quantities can be drawn from the discrete boundary integral equation. The multi-domain BFM was developed and applied to the steady state heat conduction analysis of an actual gravity dam, which contained 62 concrete layers （totally 125 domains）. In order to veri{y the result, the temperature contours of the dam were compared with the result obtained from FEM （using Abaqus）. The comparison chart has shown that the maximum temperature value of both results is 20.7℃. Moreover, the contours are highly consistent. Numerical results have demonstrated that our method can achieve comparable accuracy than other methods （e. g. the FEM） at much lower cost in terms of both computer resources and human labor.