等离子体中JEC-FDTD方法的数值色散特性和稳定性分析
发布时间：2019-01-28 11:23
【摘要】：时域有限差分(Finite-Difference Time-Domain Method,FDTD)方法是处理等离子体中电磁波传播问题的一种重要手段,其数值色散误差和稳定性是不可回避的问题。近年来随着FDTD计算方法的发展,电流密度卷积FDTD( JE Convolution FDTD, JEC-FDTD)方法在等离子体研究中得到了广泛的应用。然而,已有文献仅对非磁化等离子体中一维JEC-FDTD方法的数值色散作了分析。本文在此基础上,深入研究了等离子体中JEC-FDTD方法的数值色散特性和稳定性。具体研究内容包括:首先,介绍了 JEC-FDTD方法的基本理论,包括传统的FDTD算法及Courant稳定条件、JEC-FDTD方法的迭代方程以及完全匹配层的相关理论,并对算法进行了仿真实现;其次从一维非磁化等离子体JEC-FDTD方法的数值色散分析入手,深入研究了二维和三维情况下算法的数值色散特性,并以一维非磁化等离子体JEC-FDTD方法为例,分析了其在不同等离子体碰撞频率和不同等离子体角频率时的稳定性;最后进一步研究了一维磁化等离子体中JEC-FDTD方法的数值色散特性和稳定性,分析了磁化等离子体参数对数值色散特性和稳定性的影响。通过对非磁化等离子体和磁化等离子体中JEC-FDTD方法的数值色散特性和稳定性分析,可以得到在保证算法稳定时等离子体参数的取值范围及其数值色散误差。此研究结果对JEC-FDTD方法在等离子体中的应用具有非常重要的指导意义。此外,本文的研究思想可推广到其他色散介质的FDTD方法中。
[Abstract]:Finite difference time domain (Finite-Difference Time-Domain Method,FDTD) method is an important method to deal with electromagnetic wave propagation in plasma. The numerical dispersion error and stability are unavoidable problems. In recent years, with the development of FDTD calculation method, FDTD (JE Convolution FDTD, JEC-FDTD (current density convolution) method has been widely used in plasma research. However, only the numerical dispersion of one-dimensional JEC-FDTD method in unmagnetized plasma has been analyzed in literature. On this basis, the numerical dispersion and stability of the JEC-FDTD method in plasma are studied. The main contents are as follows: firstly, the basic theory of JEC-FDTD method is introduced, including the traditional FDTD algorithm and Courant stability condition, the iterative equation of JEC-FDTD method and the related theory of perfectly matched layer, and the simulation of the algorithm is implemented. Secondly, starting with the numerical dispersion analysis of the one-dimensional unmagnetized plasma JEC-FDTD method, the numerical dispersion characteristics of the algorithm in two and three dimensions are deeply studied, and the one-dimensional unmagnetized plasma JEC-FDTD method is taken as an example. Its stability under different plasma collision frequency and different plasma angular frequency is analyzed. Finally, the numerical dispersion and stability of the JEC-FDTD method in one-dimensional magnetized plasma are studied, and the influence of the parameters of the magnetized plasma on the numerical dispersion and stability is analyzed. By analyzing the numerical dispersion characteristics and stability of JEC-FDTD method in unmagnetized plasma and magnetized plasma, the range of plasma parameters and the numerical dispersion error can be obtained when the stability of the algorithm is guaranteed. The results are of great significance for the application of JEC-FDTD method in plasma. In addition, the idea of this paper can be extended to the FDTD method in other dispersive media.
【学位授予单位】：西安理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O53;O241.8
本文编号：2417009
[Abstract]:Finite difference time domain (Finite-Difference Time-Domain Method,FDTD) method is an important method to deal with electromagnetic wave propagation in plasma. The numerical dispersion error and stability are unavoidable problems. In recent years, with the development of FDTD calculation method, FDTD (JE Convolution FDTD, JEC-FDTD (current density convolution) method has been widely used in plasma research. However, only the numerical dispersion of one-dimensional JEC-FDTD method in unmagnetized plasma has been analyzed in literature. On this basis, the numerical dispersion and stability of the JEC-FDTD method in plasma are studied. The main contents are as follows: firstly, the basic theory of JEC-FDTD method is introduced, including the traditional FDTD algorithm and Courant stability condition, the iterative equation of JEC-FDTD method and the related theory of perfectly matched layer, and the simulation of the algorithm is implemented. Secondly, starting with the numerical dispersion analysis of the one-dimensional unmagnetized plasma JEC-FDTD method, the numerical dispersion characteristics of the algorithm in two and three dimensions are deeply studied, and the one-dimensional unmagnetized plasma JEC-FDTD method is taken as an example. Its stability under different plasma collision frequency and different plasma angular frequency is analyzed. Finally, the numerical dispersion and stability of the JEC-FDTD method in one-dimensional magnetized plasma are studied, and the influence of the parameters of the magnetized plasma on the numerical dispersion and stability is analyzed. By analyzing the numerical dispersion characteristics and stability of JEC-FDTD method in unmagnetized plasma and magnetized plasma, the range of plasma parameters and the numerical dispersion error can be obtained when the stability of the algorithm is guaranteed. The results are of great significance for the application of JEC-FDTD method in plasma. In addition, the idea of this paper can be extended to the FDTD method in other dispersive media.
【学位授予单位】：西安理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O53;O241.8
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