微分递推法在舰船静态电场深度换算中的应用研究

摘要

For the divergence and curl of electric field generated by the ship,which are zero in the converted area,the first-order vertical partial derivative of node on the measuring plane can be calculated by using the horizontal partial derivative,and the recursion relation can be formed based on the NewtonLeibniz formula.A differential conversion method is given to convert the electric field distribution on the measuring plane to that on the target plane.The feasibility of the method is proved by using the horizontal electric dipole (HED) as the basic simulating unit of ship static electric field through simulation and experiment.Further analysis shows that the converting precision and efficiency of the method can be improved by changing recursive step,node interval and the distance between the sensors and the sea bed.%根据舰船静态电场换算问题中换算区域内舰船静态电场的无源、无旋这一特性,得到网格节点处电场强度三分量的竖直方向1阶偏导数与水平方向1阶偏导数的关系.在两相邻深度平面间建立起以牛顿-莱布尼茨公式为基础的递推关系,逐层递推,实现了由测量平面场分布到目标平面场分布的换算,得到舰船静态电场深度换算的微分递推法.以舰船静态电场的基本模拟单元——水平电偶极子为对象,分别利用数值仿真和模拟实验的方式说明了微分递推换算方法的可行性,且在同等参数条件下,由远及近的换算精度要优于由近及远的换算精度.进一步分析表明,在实际应用中可以通过改变递推步长、测量平面网格节点间隔以及测量点阵的布设位置来进一步提高换算精度和效率.