求解三维麦克斯韦方程的时域无网格算法研究  

A meshless time-domain algorithm for solving the 3-D Maxwell's equations

作　　者：高煜堃[1] 陈红全[1] 

机构地区：[1]南京航空航天大学航空宇航学院,江苏南京210016

出　　处：《电波科学学报》2015年第2期257-263,共7页Chinese Journal of Radio Science

基　　金：国家自然科学基金(No.11172134);江苏高校优势学科建设工程

摘　　要：发展了用于求解三维麦克斯韦方程的时域无网格算法.算法基于生成的无网格点云,通过泰勒级数展开结合加权最小二乘逼近计算点云中心点上的空间导数,并构造近似黎曼解处理空间离散涉及的通量运算;空间离散后的半离散方程则采用四步RungeKutta格式推进求解.结合求解三维麦克斯韦方程,给出了时域无网格算法的具体实施过程,并基于发展的算法,成功地模拟出金属球、立方体及进气道模型等三维散射目标的电磁散射场,获得的雷达散射截面能与理论解、矩量法或精确控制法等结果吻合.A meshless time-domain algorithm for a solution of the 3-D Maxwell's equations is developed.The spatial derivatives related to the algorithm are approximated by using an expanded Taylor series and the weighted least square technique in each cloud of points,and then a particular approximate Riemann solver is constructed for computing the physical flux of the governing equations.After that,an explicit four-stage RungeKutta scheme is used to advance the Maxwell's equations in time.Combined with solving the 3-D Maxwell's equations,the implementations of the present algorithm are described in details.Based on the developed algorithm,numerical results for typical 3-D objects such as a metal sphere,a metal cube and an air-intake model are presented,which show that the obtained bistatic radar cross sections are in good agreement with the series solution or that of the reference.

关 键 词：时域无网格算法 麦克斯韦方程 点云 加权最小二乘 三维 

分 类 号：O441.4[理学—电磁学] O241.82[理学—物理]