一种简化的分析光纤布拉格光栅的时域有限差分束传输法

提出了一种便于分析光纤布拉格光栅(FBG)、基于强制边界条件的简化TD-FD-BPM模型.采用交替隐式法(ADIM)和综合道格拉斯(GD)法,离散化时域束传输方程,获得比普通差分格式低二阶的误差。提出并采用强制边界条件,简化了光波导分析中边界处理问题.重点讨论和确定了在此条件下激励源位置、脉冲形状和径向分布函数、连续波激励条件等.在修正的正弦脉冲激励情况下,通过离散傅利叶变换,直接得到较为理想的短FBG反射谱.此法可减少数值计算时间,直观反映光脉冲传输.     

粒子输运离散纵标方程基于界面修正的并行计算方法

为了改造粒子输运方程求解的隐式格式,研究设计适应大型并行计算机的并行计算方法,介绍一类求解粒子输运方程离散纵标方程组的基于界面修正的源迭代并行计算方法.应用空间区域分解,在子区域内界面处首先采用迎风显式差分格式进行预估,构造子区域的入射边界条件,然后,在各个子区域内部进行源迭代求解隐式离散纵标方程组.在源迭代过程中,在内界面入射边界处采用隐式格式进行界面修正.数值算例表明该并行计算方法在精度、并行度、简单性诸方面均具有良好的性质.     

热辐射输运问题的高效蒙特卡罗模拟方法

惯性约束聚变研究中,热辐射光子在介质中的输运以及热辐射光子与介质的相互作用是重要研究课题,蒙特卡罗方法是该类问题的重要研究手段之一.隐式蒙特卡罗方法虽然能正确地模拟热辐射在介质中的输运过程,但当模拟重介质(材料的吸收系数大)问题时,该方法花费的计算时间将变得很长,导致模拟效率很低.本文以离散扩散蒙特卡罗方法为基础,开发了"离散扩散蒙特卡罗方法辐射输运模拟程序",可以较好地解决重介质区的计算效率问题,但是离散扩散蒙卡罗方法在模拟轻介质区时精度不够高.辐射输运问题中通常既有轻介质也有重介质,为了能同时解决蒙特卡罗方法模拟的效率和精度问题,本文研究了离散扩散蒙特卡罗方法与隐式蒙特卡罗方法相结合的模拟方法,并提出了新的扩散区与输运区界面处理方法,研制了混合蒙特卡罗方法的辐射输运模拟程序.典型辐射输运问题模拟显示:在模拟重介质问题时,该程序能大幅缩短模拟时间,且能取得与隐式蒙特卡罗方法一致的结果;在模拟轻重介质均存在的问题时,与隐式蒙特卡罗方法相比,混合蒙特卡罗方法的模拟精度与其相当且计算效率同样能够得到显著提升.     

隐式ENO格式及其在内流问题中的应用

本文研究了文献[1]提出的隐式ENO格式,并对其隐式求解过程进行了改进,而且耦合以CSCM式的隐式特征边界处理。通过对超音速内流无粘流动(Euler方程)以及粘性流动(Navier-Stokes方程)的ENO格式数值解研究表明:改进后的格式是成功的,其稳定性好且节省内存。同时,本文也讨论了一些尚待进一步研究的问题。     

不可压缩流基于块预处理的并行有限元计算

发展了一个模拟非定常不可压缩粘性流的并行有限元求解器,时间离散使用具有二阶精度的隐式中点格式,基于三维非结构四面体网格剖分,使用高阶混合有限元离散速度场（P2）和压力场（P1）.全离散格式产生的代数方程组是大型、稀疏、非对称和病态的,基于修正的压力对流扩散预处理（PCD）和精心设计的子问题迭代执行策略,采用预处理的GMRES迭代法来高效求解线性方程组.利用相同的子问题迭代策略,同时给出基于最小二乘交换子（LSC）预处理的并行效率对比.大量数值算例验证了算法的精度、可扩展性和可靠性.三维驱动方腔流模拟结果（Re=3200.0）清晰地显示了方腔流中主涡（PE）、下游二次涡（DSE）、上游二次涡（USE）、侧壁涡（EWV）和TGL涡的存在.     

一种基于特征理论模拟凝聚炸药爆轰的单元中心型Lagrange方法

提出一种数值模拟凝聚炸药爆轰问题的单元中心型Lagrange方法.利用有限体积离散爆轰反应流动方程组,基于双曲型偏微分方程组的特征理论获得离散网格节点的速度与压力,获得的网格节点速度与压力用于更新网格节点位置以及计算网格单元边的数值通量.以这种方式获得的网格节点解是一种"真正多维"的理论解,是一维Godunov格式在二维Riemann问题的推广.有限体积离散得到的爆轰反应流动的半离散系统使用一种显-隐Runge-Kutta格式来离散求解：显式格式处理对流项,隐式格式处理化学反应刚性源项.算例表明,提出的单元中心型Lagrange方法能够较好地模拟凝聚炸药的爆轰反应流动.     

广义Zakharov-Kuznetsov方程的多辛Preissmann格式

广义Zakharov-Kuznetsov方程作为一类重要的非线性方程有着许多广泛的应用前景,基于Hamilton空间体系的多辛理论研究了广义Zakharov-Kuznetsov方程的数值解法,讨论了利用Preissmann方法构造离散多辛格式的途径,并构造了一种典型的半隐式的多辛格式,该格式满足多辛守恒律、局部能量守恒律.数值算例结果表明该多辛离散格式具有较好的长时间数值稳定性.     

非结构网格在平面叶栅内湍流流动数值模拟中的应用

1控制方程和离散方程对二维非定常可压缩粘性流体，雷诺时均Navierstokes方程可写成如下积分形式：式中，0为计算区域；＊D为区域边界；Q为守恒变量；F为通量，包括无粘通量F’和粘性通量F”。计算域采用三角形单元离散，三角形的边作为控制体边界，物理量置于单元中心。对每个三角形控制体，方程（1）可写成：·其中，Q；表示单元的守恒变量值；aC和Vi分别表示控制体的边界和面积，为计算式（2中右端值，将单元所有边界通量相加，最后可得如下方程：式中k（i）为单元边界，只，j为通过单元界面的通量，凸马为界面长度。2无粘通量本文采…     

Klein-Gordon-Schrdinger方程的辛Fourier拟谱格式(英文)

主要讨论Klein-Gordon-Schrdinger方程的Fourier拟谱辛格式,包括中点公式和Strmer/Verlet格式.首先构造一个哈密尔顿方程,针对此哈密尔顿方程,在空间方向用Fourier拟谱离散得到一个有限维的哈密尔顿系统,对此有限维系统在时间方向用Strmer/Verlet方法离散得到KGS方程的完全显式的辛格式.中点格式虽然是隐式的但效率也很高,且具有质量守恒律.数值实验表明,辛格式能够在长时间内很好地模拟各类孤立波.     

弹头激波诱导燃烧特性的数值模拟

为了研究弹头激波诱导燃烧，基于有限体积的考虑化学反应的Navier-Stokes（N-S）方程，对预混氢气-空气化学恰当比时的燃烧流场进行了数值模拟.时间项基于2阶隐式LU-SGS格式，对流项基于Steger-Warming进行离散，化学反应源项采用对角化隐式处理.首先，研究了网格对燃烧爆轰流场结构的影响，并利用Lehr实验结果验证了计算方法的可靠性；其次，研究了弹头的飞行Mach数（Ma=4.18，5.11，6.46）、弹头直径（D=5，10，15 mm）对燃烧流场稳定性的影响.研究表明:计算网格对氢气-空气爆轰流场结构影响很大；弹头直径一定时，氢气-空气燃烧流场稳定性随着飞行Mach数的增大而增强；弹头飞行Mach数一定时，氢气-空气燃烧流场稳定性随着弹头直径减小而增强.      

An Efficient Algorithm for Truncating Spatial Domain in Modeling Light Scattering by Finite-Difference Technique

The finite-difference time domain technique is one of the most robust and accurate numerical methods for the solution of light scattering by small particles with arbitrary composition and geometry. In practice, this method requires that the spatial domain for the computation of near-field be truncated. An absorbing boundary condition must be imposed in conjunction with this truncation. The performance of this boundary condition is essential to the stability of numerical computations and the reliability of results. In the present study, a new boundary condition, referred to as the mixed T algorithm, has been developed, which is a generalization of the transmitting boundary condition originally developed by Liao and co-workers. The present algorithm does not require spatial interpolation for wave values at interior grid points. In addition, it produces two minima of spurious reflections at small and large incident angles, allowing efficient absorption of the scattered waves at the boundary for large incident angles. When the third-order mixed T algorithm is used, the reflection coefficient of the boundary is less than 1% for incident angles from 0° to about 70°. We find that the numerical instability associated with the transmitting boundary condition is caused by the location-dependent amplitude of outgoing waves in the vicinity of the boundary. For this reason, the mixed T algorithm is stabilized by consistently introducing diffusive coefficients into the boundary equation. When the stabilized algorithm is applied, the near-field within the truncated domain can be computed by using single-precision arithmetic without overflows for more than 10⁵steps in the time-marching iteration. Finally, the new absorbing boundary condition is validated by carrying out numerical experiments involving the propagation of a TM wave excited by a sinusoidal point source, simultaneous simulation of the wave propagation in small and large domains, and the scattering of a TM wave by an infinite circular cylinder.     

时域有限差分法中电磁场的吸收边界条件

吸收边界条件在时域有限差分法计算电磁场中有着广泛的应用,从吸收边界所要满足的条件出发,将Lindman吸收边界条件推广,得到了便于计算的简化形式.两维数值模拟结果表明:以各种角度向左或右传播的p极化和s极化电磁波在边界面上的反射率均低于0.5%.     

基于表面阻抗边界条件的等离子体薄涂层电磁散射的时域有限差分分析

基于表面阻抗边界条件时域有限差分(FDTD)方法研究了一维斜入射情况下非磁化等离子体薄涂层涂敷金属材料的电磁散射特性, 该方法忽略对薄层背景材料进行网格剖分, 大大减少了计算量. 首先推导了理想导体涂敷等离子体薄涂层的表面阻抗频域表达式, 然后代入边界条件并变换到时域, 再用分段线性递推卷积方法将时域表达式离散得到FDTD迭代式. 编程计算了垂直及斜入射情形下的平行极化和垂直极化反射系数, 通过验证算例与解析解对比, 结果表明该方法的准确性和有效性. 最后利用该方法分析了不同入射角对反射系数的影响.     

Effects of Periodic Boundary Condition on Traffic Waves

In this paper, we use the speed-gradient model proposed by Jiang et al. [Transp. Res. B 36 （2002） 405] to study the effect of boundary condition on shock and rarefaction wave. Our numerical results show that this model can reproduce the evolution of the two traffic waves, which further proves that this model can be used to perfectly explore the consequences caused by various boundary conditions.     

粒子模拟激光斜入射边界条件的处理

讨论了电磁场模拟中的非反射边界条件,详细推导了斜入射情况非反射边界条件的有限差分格式,并在粒子模拟程序LARED-P上将其实现,同时给出了激光斜入射时的数值模拟结果.     

Exact boundary condition for time-dependent wave equation based on boundary integral

An exact non-reflecting boundary conditions based on a boundary integral equation or a modified Kirchhoff-type formula is derived for exterior three-dimensional wave equations. The Kirchhoff-type non-reflecting boundary condition is originally proposed by L. Ting and M.J. Miksis [J. Acoust. Soc. Am. 80 (1986) 1825] and numerically tested by D. Givoli and D. Cohen [J. Comput. Phys. 117 (1995) 102] for a spherically symmetric problem. The computational advantage of Ting–Miksis boundary condition is that its temporal non-locality is limited to a fixed amount of past information. However, a long-time instability is exhibited in testing numerical solutions by using a standard non-dissipative finite-difference scheme. The main purpose of this work is to present a new exact boundary condition and to eliminate the long-time instability. The proposed exact boundary condition can be considered as a limit case of Ting–Miksis boundary condition when the two artificial boundaries used in their method approach each other. Our boundary condition is actually a boundary integral equation on a single artificial boundary for wave equations, which is to be solved in conjunction with the interior wave equation. The new boundary condition needs only one artificial boundary, which can be of any shape, i.e., sphere, cubic surface, etc. It keeps all merits of the original Kirchhoff boundary condition such as restricting the temporal non-locality, free of numerical evaluation of any special functions and so on. Numerical approximation to the artificial boundary condition on cubic surface is derived and three-dimensional numerical tests are carried out on the cubic computational domain.     

1维介质光栅近场及其衍射的FDTD分析

 应用FDTD方法计算了单色平面波斜入射时1维介质光栅的近场，进而求出介质光栅的衍射效率。借助于周期边界条件，整个计算区域为周期结构的一个单元。考虑入射波在两种介质界面上会产生反射和透射，故在总场边界上引入入射波、反射波和透射波。给出了光栅单元截面为矩形和梯形的算例。该方法可用于斜入射情形下具有复杂结构和任意单元截面的介质栅近场及其衍射特性分析。     

Condition for invariant spectral degree of coherence of an electromagnetic plane wave on scattering

Within the accuracy of the first-order Born approximation, the condition for invariant spectral degree of coherence of an electromagnetic plane wave scattered from random media is presented. The condition for the electromagnetic plane wave is different from the one for the scalar plane wave. Results also indicate that, different polarizations of the incident plane wave would have essential effects on analytical forms of the condition. These effects may be due to the correlation-induced changes in the scattered spectral degree of coherence.     

Analysis of femtosecond pulsed beam propagation in dispersive directional coupler

An analysis of ultrashort-pulse interaction inside directional coupler structures having dispersive material is conveyed using the well-known finite difference time domain (FDTD) technique and time domain beam propagation method (TD-BPM). The implicit TD-BPM uses a higher-order non-paraxial equation suitable for femtosecond pulse. The result obtained by the one-way technique is verified with that of the widely used FDTD. A rigorous study is conveyed in order to distinguish material dispersion from intermodal dispersion. The analysis reveals that material dispersion causes energy loss in the device, in addition to extra pulse broadening and splitting that occur to a low extent in the case of intermodal dispersion.