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Analyze the singularity of the heat flux with a singular boundary element

机译：用奇异边界元件分析热通量的奇点

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摘要

In the steady state heat conduction problem, the heat flux could be infinite at the re-entrant corner, at the point where the boundary condition is discontinuous, or at the place where the material properties are changing abruptly. The conventional numerical methods, such as the finite element method (FEM) and the boundary element method (BEM), have difficulties in analyzing the singular heat flux field. Herein, a new singular element employed in the boundary integral equation is developed to interpolate the heat flux field near the singular point. The shape function of the singular element is set as an asymptotic expansion model with respect to the distance from the singular point. The singular order in the asymptotic expansion can be determined by solving the singularity eigen equation on the basis of the interpolating matrix method. The self-adaptive co-ordinate transformation method is introduced to deal with the weakly singular integral in the proposed method. Benefited from the singular element, more accurate temperature and heat flux results near the singular point are obtained with fewer elements. In addition, the proposed method is easy to be coupled with the conventional BEM without too much modifications.
机译：在稳态导热问题中，热通量可以在重新进入角处是无限的，在边界条件是不连续的，或者在材料特性突然改变的地方。传统的数值方法，例如有限元方法（FEM）和边界元法（BEM）在分析奇异热通量场方面具有困难。这里，开发了在边界积分方程中采用的新奇异元素以在奇异点附近插入热通量场。奇异元素的形状函数相对于奇异点的距离设定为渐近膨胀模型。通过基于插值矩阵方法求解奇异性特征方程，可以确定渐近膨胀中的奇异顺序。引入自适应协调转换方法以处理所提出的方法中的弱奇异积分。从奇异元素中受益，用较少元素获得奇点附近的更精确的温度和热通量。此外，该方法易于与传统BEM耦合而无需过多的修改。

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