随机媒质的时域有限差分法电磁特性分析

发布时间：2018-02-24 15:27

本文关键词： 随机FDTD 多项式混沌高超声速飞行器随机等离子体共形FDTD　出处：《南京理工大学》2017年硕士论文　论文类型：学位论文

【摘要】：时域有限差分算法以其原理简单编程容易,易获得目标的宽频带信息等优势,受到广大电磁学研究者的关注。但是由于采用Yee网格计算,在处理弯曲表面目标时会产生阶梯近似误差。因此,共形技术被提出,用于减少这种阶梯近似误差。时域有限差分方法(FDTD)已经被广泛地应用于电磁波在等离子体中传播时电磁特性分析的研究中。传统方法分析等离子体电磁特性时,没有考虑等离子体电子浓度随机变化的特性。因此本文介绍了基于多项式混沌展开的随机FDTD方法,该方法对随机变量电子浓度进行埃尔米特多项式展开和伽辽金测试,分析电子浓度随机变化时输出场值的均值和方差。该算法的精度取决于埃尔米特多项式的项数,项数越高精度越高,消耗的时间也随之变多。本文首先用磁化等离子体预测校正法分析了磁化等离子体的电磁散射特性,在此基础上加入了多项式混沌展开的随机FDTD算法,接着用共形FDTD分析了随机磁化等离子体模型的电磁特性。用非磁化等离子体龙格库塔指数时呈差分法分析了非磁化等离子体的电磁散射特性,继而用共形FDTD分析了高超声速目标的电磁散射特性,在此基础上加入了多项式混沌展开的随机FDTD算法,最后对高超声速目标周围产生的随机非均匀等离子体流场的电磁特性进行共形FDTD分析。
[Abstract]:The finite difference time-domain (FDTD) algorithm has attracted the attention of many electromagnetic researchers because of its advantages of simple programming and easy access to target broadband information. However, due to the use of Yee grid computing, the finite difference time-domain (FDTD) algorithm has attracted the attention of many electromagnetic researchers. The ladder approximation error occurs in the treatment of curved surface targets. Therefore, conformal techniques have been proposed. The finite difference time-domain (FDTD) method has been widely used in the analysis of electromagnetic characteristics of electromagnetic waves propagating in plasma. The random FDTD method based on polynomial chaotic expansion is introduced in this paper. The Hermitian polynomial expansion and Galerkin test for the electron concentration of random variables are presented in this paper. The mean and variance of the output field value are analyzed when the electron concentration varies randomly. The accuracy of the algorithm depends on the number of terms of the Hermite polynomial, and the higher the term number is, the higher the precision is. In this paper, the electromagnetic scattering characteristics of magnetized plasma are analyzed by using the predictive correction method of magnetized plasma, and the stochastic FDTD algorithm based on polynomial chaotic expansion is added. Then the electromagnetic characteristics of the random magnetized plasma model are analyzed by conformal FDTD, and the electromagnetic scattering characteristics of the unmagnetized plasma are analyzed by using the Runge-Kutta exponent of the unmagnetized plasma as a difference method. Then the electromagnetic scattering characteristics of hypersonic targets are analyzed by conformal FDTD, and the stochastic FDTD algorithm based on polynomial chaotic expansion is added. Finally, the electromagnetic characteristics of a random inhomogeneous plasma flow around a hypersonic target are analyzed by conformal FDTD.
【学位授予单位】：南京理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TN011

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