【摘要】：時(shí)域有限差分(Finite-Difference Time-Domain Method,FDTD)方法是處理等離子體中電磁波傳播問題的一種重要手段,其數(shù)值色散誤差和穩(wěn)定性是不可回避的問題。近年來隨著FDTD計(jì)算方法的發(fā)展,電流密度卷積FDTD( JE Convolution FDTD, JEC-FDTD)方法在等離子體研究中得到了廣泛的應(yīng)用。然而,已有文獻(xiàn)僅對(duì)非磁化等離子體中一維JEC-FDTD方法的數(shù)值色散作了分析。本文在此基礎(chǔ)上,深入研究了等離子體中JEC-FDTD方法的數(shù)值色散特性和穩(wěn)定性。具體研究?jī)?nèi)容包括:首先,介紹了 JEC-FDTD方法的基本理論,包括傳統(tǒng)的FDTD算法及Courant穩(wěn)定條件、JEC-FDTD方法的迭代方程以及完全匹配層的相關(guān)理論,并對(duì)算法進(jìn)行了仿真實(shí)現(xiàn);其次從一維非磁化等離子體JEC-FDTD方法的數(shù)值色散分析入手,深入研究了二維和三維情況下算法的數(shù)值色散特性,并以一維非磁化等離子體JEC-FDTD方法為例,分析了其在不同等離子體碰撞頻率和不同等離子體角頻率時(shí)的穩(wěn)定性;最后進(jìn)一步研究了一維磁化等離子體中JEC-FDTD方法的數(shù)值色散特性和穩(wěn)定性,分析了磁化等離子體參數(shù)對(duì)數(shù)值色散特性和穩(wěn)定性的影響。通過對(duì)非磁化等離子體和磁化等離子體中JEC-FDTD方法的數(shù)值色散特性和穩(wěn)定性分析,可以得到在保證算法穩(wěn)定時(shí)等離子體參數(shù)的取值范圍及其數(shù)值色散誤差。此研究結(jié)果對(duì)JEC-FDTD方法在等離子體中的應(yīng)用具有非常重要的指導(dǎo)意義。此外,本文的研究思想可推廣到其他色散介質(zhì)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.
【學(xué)位授予單位】：西安理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O53;O241.8

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