基于圆环坐标系的三维静电场曲边三角形边界元方法

Curve Element BEM in 3-D Electrostatic Fields Based on Ring Coordinate Systems

针对高压电力设备中常见的圆环电极表面电场强度的计算问题,提出了圆环面曲边三角形边界元方法。在该方法中,单元积分严格在圆环表面上进行,求解函数在圆环面曲边三角形单元上沿圆环坐标线性插值,边界单元的外法线方向严格取为圆环面的外法线方向。算例计算结果表明,与直边三角形边界元相比,在网格剖分节点分布相同的情况下,圆环面曲边三角形边界元计算精度显著提高;在计算精度要求相同的情况下,采用圆环面曲边三角形边界元计算,节点数可以大幅度减少,从而对计算机内存需求明显减少,总体计算时间也相应减少。

The torus curve triangular BEM is put forward to calculate electric field intensity of ring electrodes in 3-D electrostatic fields. In this method, the element integral is strictly carried through on the torus, and the solved function is linearly interpolated on torus curve element along the ring coordinates, and directions of outward normal line to element and torus are strictly unanimous. The calculated results show that the precision of the torus curve triangular BEM is obviously higher than plane triangular BEM on the condition of the same nodes; and on the condition of the same precision the torus curve triangular BEM requires less nodes, consequently required memory and calculated time can be decreased greatly.