一般正交曲线坐标系中的WEFDTD  

WEFDTD in Generalized Orthogonal Coordinates

作　　者：王建永[1] 李庆武[2] 刘国高[1] 

机构地区：[1]河海大学数理部,江苏常州213022 [2]河海大学计算机与信息工程学院,江苏常州213022

出　　处：《计算机仿真》2007年第2期69-71,共3页Computer Simulation

基　　金：河海大学青年教师学术能力培养基金项目(XZX/CGA023)

摘　　要：相对于时域有限差分法,波动方程时域有限差分法(WEFDTD)具有程序简单、节约内存和机时等优势,但目前WEFDTD的应用还局限于直角坐标系,计算精度也只有二阶。为了把WEFDTD推广到一般正交曲线坐标系(GOC),在GOC中用中心差分离散波动方程,得到了GOC中具有二阶精度的WEFDTD迭代公式。为了提高计算精度,用泰勒公式和波动方程把对时间的导数转化为对空间的导数,用具有高阶精度的导数近似公式替代泰勒公式和波动方程中对空间的导数,实现了GOC中的WEFDTD的高阶算法。相对于具有二阶精度的算法,高阶算法没有增加存储量。数值实验证实了方法的有效性。Wave equation finite - difference time - domain method（WEFDTD） has the advantages of simpler program, less computer memory and computational burden in comparison with finite - difference time - domain method（FDTD）, but application of WEFDTD is confined to Cartesian coordinate, and computational accuracy is only 2 - order currently. In order to popularize WEFDTD to generalized orthogonal coordinates（GOC）, wave equation in GOC is discreted by using central difference, so iterative equation with 2 - order computational accuracy in GOC is obtained. To enhance the computational accuracy, derivative for time is transformed into derivatives for space by using Tailor series and wave equation, and derivatives for space in Tailor series and wave equation are substituted by approximate equation with higher - order computational accuracy, so higher - order algorithm of WEFDTD in GOC is implemented. In comparison with 2 - order algorithm, higher - order algorithms needn＇t add computer memory. The validity of the approach is verified by numerical experiments.

关 键 词：波动方程时域有限差分法 正空曲线坐标系 高阶算法 

分 类 号：TP391.9[自动化与计算机技术—计算机应用技术]