三维瞬态导热温度场边界元计算及一阶数学奇异的处理

A BOUNDARY ELEMENT INVESTIGATION OF 3-DIMENSIONAL TRANSIENT HEAT CONDUCTION AND THE TREATMENT OF SINGULARITY

推导了三维瞬态导热温度场边界元解法的积分方程和离散代数方程,并编制了相应的计算机程序,采用坐标变换的解析消去法,处理边界元的一阶数学奇异点,从而提高了算法的数值精度。用本程序计算了正方体和圆柱环瞬态导热温度场,数值解与解析解的吻合程度令人满意。

The 3-dimensional transient heat conductions in a cylinder and in a cube are numerically calculated using Boundary Element Method in the present study. To promote the accuracy of scheme, the analytical treatment is introduced to deal with mathematical singularity occured in Boundary Element Method. Comparing with analytical solutions, the numerical results are quite good.