坐席低谷效应的时域有限差分多项模拟

介绍了交错网格下,以声压和质点振动速度为声场参量的室内声学时域有限差分递推格式,给出了在建筑边界截断计算区域的边界条件差分格式。在水平地面房间模型下,应用时域有限差分法模拟了坐席低谷效应对于空间和时间的多种特性;此外,模拟了地面起坡时的低谷效应。     

基于SNGR方法的后缘噪声数值模拟

采用随机噪声产生和传播(SNGR)方法对后缘噪声进行数值模拟.SNGR方法结合随机方法和计算流体力学,耗费较少的计算资源就可以预测噪声水平.数值模拟时采用有限体积法求解雷诺平均Navier-Stokes(RANS)方程;采用有限差分法求解声学扰动方程,数值格式采用色散关系保持(DRP)格式,远场边界条件采用无反射边界条件.以二维平板和NACA0012翼型为例,编制程序,与参考结果对比表明,程序可以预测后缘噪声.     

蜂巢晶格光子晶体能带特性的研究

运用时域有限差分法数值模拟了蜂巢晶格光子晶体能带特性,得到了蜂巢晶格光子晶体的最大横电(TE)模、横磁(TM)模和完全带隙,研究结果为光子晶体器件的开发提供了理论依据.     

有限长导体棒的电荷分布的数值模拟

利用有限差分法对有限长导体棒电荷面密度进行了数值模拟.数值模拟结果说明,有限长带电导体棒面电荷分布不仅与导体表面的曲率半径有关,还与导体的总体形状以及导体周围环境中其他导体的分布有关.     

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用时域有限差分法研究了电磁波在等离子体光子晶体中的传播特性。数值模拟中使用完全匹配层吸收边界条件,计算了电磁波通过等离子体光子晶体的反射和透射系数。讨论了等离子体密度、等离子体温度、介电常数比和引入缺陷层对等离子体光子晶体光子带隙的影响。     

亚波长衍射微透镜色散的数值分析

采用旋转体时域有限差分法对亚波长衍射微透镜进行数值分析，给出了在微透镜焦平面上的电场强度分布和从近场到远场的电场强度分布. 研究了亚波长衍射微透镜的色散，给出了入射波长不同于设计波长的色散曲线，数值分析结果表明了亚波长衍射微透镜的负向色散特性，而且随着波长的减小焦距增加得更快. 关键词： 亚波长衍射微透镜 色散 时域有限差分法     

同心方槽电场的实验模拟和数值求解

对同心槽内静电场用稳恒电场进行实验模拟，并以有限差分法进行数值计算，由计算结果绘制出横截面内电势随场点变化的立体和等势经平在图，将实验模拟和数值计算进行比较。     

双折射光子晶体光纤传输特性分析

采用时域有限差分法对光子晶体光纤导模的传输特性进行数值分析,通过该法可得到任意横向结构光子晶体光纤的色散特性和双折射特性。为提高精度,在计算中应用了各向异性完全匹配层作为吸收边界条件。光子晶体光纤的传输特性完全由其横向结构决定。用时域有限差分法对一类对称结构和两类非对称结构光子晶体光纤进行了数值分析,计算结果表明经合理设计的非对称结构光子晶体光纤中可存在较高的双折射(其双折射可达0．07)。表明时域有限差分法可有效应用于分析和设计具有特定色散和偏振特性的光子晶体光纤。     

用二维时域有限差分法分析条形多层波导

为精确分析条形多层波导和多量子阱波导，本文提出了一种以二维时 限差分法为基础的全波数值方法，给出了场分布的色散特性的数值结果，并与矢量有限元法已有的结果作了比较；文中还研究了以二维时域有限差分法为基础的标量近似技术，提出了它的有效性和精度的局限性。     

二维光子晶体T型波导分支器数值模拟研究

采用平面波展开法和时域有限差分法,对GaAs二维正方晶格光子晶体的色散特性和带隙结构进行了数值模拟研究,并对GaAs二维光子晶体线缺陷构成的T型波导分支器的微波传输特性进行了模拟和优化。数值模拟结果表明,光子晶体填充比对带隙结构有显著地影响。通过在拐角处插入额外的电介质棒对GaAs二维正方光子晶体T型波导分支器进行优化,数值模拟的结果表明,优化的GaAs二维正方光子晶体T型波导分支器在一阶带隙范围内透射系数将提高到0.96以上。     

基于Liao氏吸收边界条件的四阶FDTD算法

建立了在空间上用四阶差分的时域有限差分法的 Liao氏吸收边界,证明了四阶差分具有比二阶差分更小的数值色散.空间上用四阶差分的时域差分法将有助于人们对尺寸较大的物体如光纤等光波导的数值分析.     

A method of solving the stiffness problem in Biot＇s poroelastic equations using a staggered high-order finite-difference

In modelling elastic wave propagation in a porous medium, when the ratio between the fluid viscosity and the medium permeability is comparatively large, the stiffness problem of Blot＇s poroelastic equations will be encountered. In the paper, a partition method is developed to solve the stiffness problem with a staggered high-order finite-difference. The method splits the Biot equations into two systems. One is stiff, and solved analytically, the other is nonstiff, and solved numerically by using a high-order staggered-grid finite-difference scheme. The time step is determined by the staggered finite-difference algorithm in solving the nonstiff equations, thus a coarse time step may be employed. Therefore, the computation efficiency and computational stability are improved greatly. Also a perfect by matched layer technology is used in the split method as absorbing boundary conditions. The numerical results are compared with the analytical results and those obtained from the conventional staggered-grid finite-difference method in a homogeneous model, respectively. They are in good agreement with each other. Finally, a slightly more complex model is investigated and compared with related equivalent model to illustrate the good performance of the staggered-grid finite-difference scheme in the partition method.     

Extending Anisotropic Perfectly Matched Layer Absorbing Boundary Condition to Biaxial Media

The absorbing boundary condition required for an anisotropic perfectly matched layer for materials that exhibit a uniaxial and biaxial permittivity tensor is investigated. These materials are used in optical and millimeter wave devices and other particular situations such as in the construction of modern aircraft and automobiles. The derivation presented in this paper may be not suitable for all the arbitrary orientations but for many common situations. The effectiveness of the condition is also illustrated with examples by the finite-difference and finite-element method.     

Modal Analysis of Nonuniformly Dielectric Waveguide Using Semivectorially Compact Finite-Difference Time-Domain Method

A compact two-dimensional finite-difference time-domain method is developed for the modal analysis of nonuniform dielectric waveguides. The unsplit-field perfectly-matched-layer absorbing boundary condition has also been extended to this approach. The proposed method approximates the maxwell equations by using the semivectorial wave equations, and the dominant electric fields are solved for two perpendicular polarizations. By introducing the new techniques, complex variables can be avoided in the calculations. At the same time, the number of variables is minimized in the computation domain. Through that, approximately half of the computation effort can be saved without accuracy loss. Numerical examples are given to substantiate the theory. Excellent accuracy has been obtained for the entire frequency spectrum, even near the cutoff region.     

旋转体时域有限差分法的另一推导方法和单向波方程吸收边界条件

提出了旋转体时域有限差分法的另一推导方法.基于这一方法,推导了旋转体电磁波的波动方程,进一步得出了旋转体时域有限差分法的单向波方程吸收边界条件.数值实验证实了该吸收边界条件的正确性.     

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.     

2.5维圆波导开放边界截断的修正完全匹配层方法

 在时域有限差分算法中，完全匹配层是一种高效的吸收边界条件。通过在标准完全匹配层(PML)方程中添加具有物理意义的电导率和导磁率附加项，提出了修正完全匹配层(MPML)方法，给出了圆柱坐标下3维MPML方程，并应用于2.5维圆波导开放边界的截断计算。计算结果表明，在不同频率和模式的激励下，加入平滑电导率和导磁率附加项后，与标准PML方法相比，MPML方法的相对误差降低8~10 dB。     

Low group velocity in a photonic crystal coupled-cavity waveguide

A two-dimensional photonic crystal coupled-cavity waveguide is designed and optimized, the transmission spectrum is calculated by using the finite-difference time-domain method, and the group velocity of c/1856 is obtained. To our knowledge, this value of group velocity is the lowest group velocity in a photonic crystal waveguide calculated from its transmission spectrum so far. The result is confirmed by the photonic band structure calculated by using the plane wave expansion method, and it is found that the photonic crystal waveguide modes in a photonic band structure are in accordance with those in the transmission spectrum by using the finite-difference time-domain method. The mechanism of slow light in the coupled-cavity waveguide of photonic crystal is analysed.     

NS方程的各向异性笛卡尔网格法研究

将近年发展起来的用于Euler方程求解的具有局部均匀网格总体非结构特性的笛卡尔网格法推广到NS方程的求解。为了与流场的各向异性相适应、减少网格点数量,提出了一种各向异性网格加密法。另外还研究了分级笛卡尔网格对内点格式稳定性的影响和插值固体边界条件的稳定性。数值结果表明各向异性笛卡尔网格法相对于传统的各向同性网格方法能大量节省网格点数量而且与后者具有同样的精度。