Fast High Order Algorithm for Three-Dimensional Helmholtz Equation Involving Impedance Boundary Condition with Large Wave Numbers

Acoustic fields with impedance boundary conditions have high engineering applications, such as noise control and evaluation of sound insulation materials, and can be approximated by three-dimensional Helmholtz boundary value problems. Finite difference method is widely applied to solving these problems due to its ease of use. However, when the wave number is large, the pollution effects are still a major difficulty in obtaining accurate numerical solutions. We develop a fast algorithm for solving three-dimensional Helmholtz boundary problems with large wave numbers. The boundary of computational domain is discrete based on high-order compact difference scheme. Using the properties of the tensor product and the discrete Fourier sine transform method, the original problem is solved by splitting it into independent small tridiagonal subsystems. Numerical examples with impedance boundary conditions are used to verify the feasibility and accuracy of the proposed algorithm. Results demonstrate that the algorithm has a fourth- order convergence in and -norms, and costs less CPU calculation time and random access memory.

Power and Cross-Spectra for the Turbulent Atmospheric Motion and Transports in the Domain of Wave Number Frequency Space: Theoretical Aspects

The study of large-scale atmospheric turbulence and transport processes is of vital importance in the general circulation of the atmosphere. The governing equations of the power and cross-spectra for the atmospheric motion and transports in the domain of wave number frequency space have been derived. The contributions of the nonlinear interactions of the atmospheric waves in velocity and temperature fields to the conversion of kinetic and potential energies and to the meridional transports of angular momentum and sensible heat in the atmosphere have been discussed.

Wave Number Method for Three-Dimensional Steady-State Acoustic Problems

Based on the indirect Trefftz approach, a wave number method （WNM） is proposed to deal with three-dimensional steady-state acoustic problems. In the WNM, the dynamic pressure response variable is approximated by a set of wave functions, which exactly satisfy the Helmholtz equation. The set of wave functions comprise the exact solutions of the homogeneous part of the governing equations and some particular solution functions. The unknown coefficients of the wave functions can be obtained by enforcing the pressure approximation to satisfy the boundary conditions. Compared with the boundary element method （BEM）, the WNM have a smaller system matrix, and is applicable to the radiation problems since the wave functions are independent of the domain size. A 3D acoustic cavity is exemplified to show the properties of the method. The results show that the wave number method is more efficient than the BEM, and it is fairly accurate.

Modal Wave Number Spectrum for Mesoscale Eddies

The variations of ocean environmental parameters invariably result in variations of local modal wave numbers of a sound pressure field. The asymptotic Hankel transform with a short sliding window is applied to the complex sound pressure field in the water containing a mesoscale eddy to examine the variation of local modal wave numbers in such a range-dependent environment. The numerical simulation results show that modal wave number spectra obtained by this method can reflect the location and strength of a mesoscale eddy, therefore it can be used to monitor the strength and spatial scale of ocean mesoscale eddies.

Modal Wave Number Tomography and Bottom Parameter Dependence

A shallow water tomography scheme based on the modal wave number inversion technique is considered in this paper. The scheme is based on the assumption that modal wave number for trapped modes can be measured in a suitable way. The tomographic inversion is accomplished in two steps: firstly, the bottom parameters are inverted by using the bottom reflection phase shift with the known sound speed profile; secondly, the variation of sound speed profile at different time is inverted provided the bottom parameters are known. A numerical simulation shows that the proposed scheme works well, and the sensitivity analysis of sound speed profile inversion is performed for shallow water environmental parameters: sound speed, density and attenuation coefficient of the bottom.

A Numerical Analysis of the Weak Galerk in Method for the Helmholtz Equation with High Wave Number

We study the error analysis of the weak Galerkin finite element method in[24,38](WG-FEM)for the Helmholtz problem with large wave number in two and three dimensions.Using a modified duality argument proposed by Zhu and Wu,we obtain the pre-asymptotic error estimates of the WG-FEM.In particular,the error estimates with explicit dependence on the wave number k are derived.This shows that the pollution error in the broken H1-norm is bounded by O(k(kh)^(2p))under mesh condition k^(7/2)h^(2)≤C0 or(kh)^(2)+k(kh)^(p+1)≤C_(0),which coincides with the phase error of the finite element method obtained by existent dispersion analyses.Here h is the mesh size,p is the order of the approximation space and C_(0) is a constant independent of k and h.Furthermore,numerical tests are provided to verify the theoretical findings and to illustrate the great capability of the WG-FEM in reducing the pollution effect.

Changes of infrared absorption wave number of aromatic-ring C=C bond of vitrinite and their significance

The humilith series of lignite, longflame coal, gas coal, fat coal, coking coal, lean coal, meagre coal and anthracite are measured by FIR1600 infrared spectrophotometer. The variation curve between the infrared absorption wave number of aromaticring C--C bond of vitrinite and its reflectance values are gained, which shows the shift of infrared absorption wave number of aromaticring C--C bond of humic coals towards lower wave number with the increase of coalification. It is believed that the coal rank of humilith series can be determined and more evolutional information about coal composition and structure can be obtained by the infrared spectroscopic method.

Effect of Particle Number Density on Wave Dispersion in a Two-Dimensional Yukawa System

Effect of the particle number density on the dispersion properties of longitudinal and transverse lattice waves in a two-dimensional Yukawa charged-dust system is investigated using molecular dynamics simulation. The dispersion relations for the waves are obtained. It is found that the frequencies of both the longitudinal and transverse dust waves increase with the density and when the density is sufficiently high a cutoff region appears at the short wavelength. With the increase of the particle number density, the common frequency tends to increase, and the sound speed of the longitudinal wave also increases, but that of the transverse wave remains low.

Wave-current interaction with a vertical square cylinder at different Reynolds numbers

Large eddy simulation is performed to study three-dimensional wave-current interaction with a square cylinder at different Reynolds numbers, ranging from 1,000 to 600,000. The Keulegan-Carpenter number is relevantly a constant of 0.6 for all cases. The Strouhal number, the mean and the RMS values of the effective drag coefficient in the streamwise and transverse directions are computed for various Reynolds numbers, and the velocity of a rep- resentative point in the turbulent zone is simulated to find the turbulent feature. It is found that the wave-current interaction should be considered as three-dimensional flow when the Reynolds number is high; under wave-current effect, there exists a critical Reynolds number, and when the Reynolds number is smaller than the critical one, current effect on wave can be nearly neglected; conversely, with the Reynolds number increasing, wave-currentstructure interaction is sensitive to the Reynolds number.

GPR信号去噪的变分模态分解

为了进一步提高探地雷达(ground penetrating radar,GPR)数据的信噪比,压制由随机扰动引起的随机绕射能量,将二维变分模态分解(two-dimensional variational mode decomposition,2D-VMD)引入二维GPR数据的噪声压制处理中。首先,对GPR数据进行2D-VMD处理,并分析各阶本征模态函数(intrinsic mode function,IMF)分量及其对应的频率-波数域谱来确定雷达剖面中的各回波类型。然后,计算IMF分量与原始数据的互相关系数来确定信号模态和噪声模态,并对信号模态进行重构得到降噪后的数据。理论数据和实测数据测试表明,相比于传统的1D-VMD法,2D-VMD滤波后的含噪正演记录峰值信噪比由6.44 dB增加到7.72 dB;经2D-VMD降噪处理后的雷达剖面在保留有效信号的基础上,可以有效压制随机扰动带来的噪声,并且得到的雷达剖面同相轴连续性更好。

社区尺度斜入射波场下场地-建筑群耦合作用模拟方法

场地-城市相互作用(site-city interaction,SCI)效应会显著改变场地地震波场分布及建筑反应,基于SCI效应理论计算研究方法的发展现状,发挥谱元(spectral element,SE)法可快速高效求解三维地震波场传播和多自由度(multi-degree of freedom,MDOF)模型计算量小且可同时模拟大量建筑的优势,同时,结合频率波数域(frequency wave number analysis,FK)方法,以等效地震荷载的方式施加地震波场,建立了FK-SE-MDOF耦合方法,实现了SE-MDOF耦合模型中多种波型(P波、SV波和SH波)的斜入射输入,解决了当前三维SCI效应研究方法中未能同时考虑建筑非线性、频谱特性、地震波波型及入射角度影响的问题。首先对方法原理进行了介绍;然后,通过与振动台试验的对比,验证了方法的正确性;进而,采用该方法建立理想场地-城市建筑群相互作用耦合模型,主要探讨了入射角度和地震波波型对SCI效应的影响,得到了一些有益结论。该方法较为真实地反映SCI效应影响的同时,可反映建筑基础轮廓对地震波场的影响,适用于需考虑建筑轮廓信息的社区尺度SCI效应研究,可为城市规划、抗震设计、风险评估以及震后救援等工作提供定量指导。

Travelling Waves: Interplay of Low to High Reynolds Number and Tan-Cot Function Method to Solve Burger’s Equations

We study the nonlinear parabolic equations for travelling wave solutions of Burger’s equations. The purpose of the present work is to study various types of Burger’s equations describing waves and those are based on nonlinear equations. We focus on to describe the analytic solution in the special pattern of travelling wave solutions using tan-cot function method. We discuss about inviscid and viscous version of Burger’s equation for fluid flow and investigate the effects of internal friction of a fluid via Reynolds number. By changing the velocity amplitude, the nature of flows with shock wave and disturbance are observed. For numerical solutions, the Crank-Nicolson scheme is introduced to establish the wave solutions.

双波长近红外拉曼光谱仪及在腐蚀产物分析中的应用

在拉曼光谱测试中某些物质存在荧光发射背景,由于荧光强度一般比拉曼散射强度高几个数量级,在荧光干扰时几乎无法获得有效的拉曼光谱信号。为抑制荧光背景,可选用近红外波段激光作为激发光源,而硅基探测器在1 000 nm以上波段时光量子效率严重下降,导致近红外拉曼光谱仪器难以探测3 000 cm^(-1)以上的波段,存在荧光抑制效果与检测范围无法兼顾的问题。由于高波数的拉曼特征峰是识别材料种类和解析材料结构的重要依据,如氨基的N—H伸缩振动峰在3 300 cm^(-1)附近、 OH-伸缩振动峰在3 650 cm^(-1),这些基团是分析材料腐蚀产物、水合物、有机物等的重要依据。因此,迫切需要开发一种解决拉曼光谱仪器无法兼顾荧光抑制效果和检测光谱范围问题的方法。该工作提出一种采用光谱仪固定检测波段、 730和830 nm双波长激光“接力”激发的方案(即830 nm激发低波数拉曼、 730 nm激发高波数拉曼)。通过双激光波长“接力”激发、固定检测波段的新设计,可有效拓宽检测范围至200~3 700 cm^(-1),并且不会降低光谱分辨率(达到6 cm^(-1)),与此同时整机光路无机械可动部件,可靠性高便于实现便携式设计。通过样机进行测试,证明该技术方案具备高灵敏度、较好荧光抑制效果、宽检测范围和较高光谱分辨率等优势。通过研制的双波长近红外拉曼光谱仪获得了铀腐蚀产物、有机涂层下的LiH潮解产物的清晰拉曼信号,解决了特种材料无损检测的技术难题。该技术也适用于其他研究及检测领域,特别是拉曼散射截面小、荧光背景高的物质检测。由于双波长近红外拉曼光谱仪可覆盖200~3 700 cm^(-1)检测范围,为多数水合物、含羟基及氨基官能团物质的拉曼检测提供了一种可行的技术途径。

Numerical Simulation for Refraction-Diffraction of Waves in Water of Slowly Varying Current and Topography

A new numerical finite difference iteration method for refraction-diffraction of waves ia water of slowly varying current and topography is developed in this paper. And corresponding theoretical model including the dissipation term is briefly described, together with some analysis and comparison of computational results of the model with measurements in a hydraulic scale model (Berkhoff et al., 1982). An example of practical use of the method is given, showing that the present model is useful to engineering practice.

供电电源系统电能质量稳定性监测方法

监测供电电源系统电能质量是保障电力系统与用户侧设备安全运行的有效方法,为保障供电电源系统电能质量,研究供电电源系统电能质量稳定性监测方法。基于希尔伯特-黄变换HHT(Hilbert-Huang transform)算法监测供电电源系统电能质量信号帧中谐波频率与幅值,并检测电能质量扰动信号的扰动时间幅值与频率等,以此实现监测系统电能质量稳定性。通过实验检测不同压力(不同电能质量信号帧数量)条件下监测到的电能质量信号的丢帧率和准确率及电能质量信号传输时延,测试结果显示所研究方法可实现电能质量的监测。

流动介质中板状结构辐射声功率研究

由对流波动方程和欧拉方程,本文推导了流动介质中区分传播波和倏逝波的辐射椭圆方程及板状结构辐射声功率计算公式。基于该公式,通过提取辐射椭圆内的传播波波数对应的表面法向振速波数域频谱,可实现流动介质中板状结构辐射声功率的计算。基于辐射椭圆方程,明确了介质流动对板状结构辐射声功率产生影响的机理。最后,以简支板为对象,通过数值仿真对比了不同流速下的辐射声功率,结果表明了考虑介质流动影响的必要性及其对声功率的影响规律。

爆炸冲击波超压非均匀分布特性及最优测点数量

为掌握炸药爆炸冲击波超压的非均匀分布特性,根据非理想爆轰波特征及空气冲击波的形成机制,探讨了炸药爆炸冲击波超压峰值时空非均匀分布的原因和表现形式,得到了实验影像和测试数据的验证;开展了公斤级和百公斤级装药爆炸冲击波实验,分析了相同对比距离的多个超压峰值测试结果之间的偏离特性,结果表明炸药组分非理想程度越高、装药质量越大、距离装药越近,冲击波超压峰值非均匀特征越显著。在实验数据偏离分析基础上,提出了满足非均匀分布超压准确测试的最优测点数量,将爆炸场划分为对比距离小于1.5 m/kg^(1/3)、1.5~3.0 m/kg^(1/3)、3~5 m/kg^(1/3)和大于5 m/kg^(1/3)共4个区域,对应的最优测点数量分别为6个、5个、4个和2个。

裂缝等效宽度的斯通利波检测实验及反演

为了破解裂缝地层识别与评价的难题,进行缩比例模型井声波测量物理实验,结合数值模拟分析不同裂缝宽度和条数下斯通利波特征,总结水平裂缝不同宽度及条数对斯通利波衰减的影响规律,提出裂缝等效宽度的概念,定量表征裂缝带对斯通利波幅度的影响,建立基于裂缝等效宽度的反演方法和流程。研究结果表明:随着裂缝等效宽度的增大,直达斯通利波幅度呈指数规律减小;在裂缝等效宽度保持不变的情况下,裂缝条数越多,直达斯通利波幅度越大;利用裂缝等效宽度能够实现裂缝带的定量表征。

长矩形腔体中混合流体的双局部行波

基于数值模拟,研究了分离比ψ=-0.4和长高比Γ=40的腔体内的双局部行波对流的动力学特性。结果发现,对流圈在端壁产生,向中心传播,到达一定位置对流圈消失;在矩形腔体中两端壁附近行波对流区域与中间部位无对流的传导区域同时共存,形成双局部行波对流;双局部行波对流中的行波由腔体两端向中部传播;腔体二分之一高度处的温度与垂直流速分布是谐波结构,波形比较光滑,浓度分布是台型结构;随着时间的发展,垂直流速最大值稳定在某个数值周期变化,下壁面努塞尔数基本稳定在某个数值,垂直流速最大值和下壁面努塞尔数及其达到稳定的时间随着相对瑞利数r的增加而增加;双局部行波对流稳定的存在于相对瑞利数r∈{1.52,1.57]的区间,双局部行波的对流区长度随着相对瑞利数r的增加呈良好的增加关系,并给出了双局部行波的对流区长度随着相对瑞利数r变化的拟合关系式。

湍流普朗特数在高超声速绕流中的修正

为精确模拟高超声速激波/湍流边界层干扰导致的复杂非平衡湍流流动,提出一种湍流普朗特数修正模型。应用数值模拟及理论分析方法,对高超声速来流马赫数为9.22的平板、压缩拐角等绕流进行数值分析,评估了所提出的湍流普朗特数修正模型。数值模拟结果与实验数据及Kays湍流普朗特数模型的对比表明:对高超声速复杂流动,湍流普朗特数应进行修正,提出的经湍流非平衡参数修正的湍流普朗特数修正模型与原模型及Kays模型相比,给出的壁面压强、壁面热流更精确,壁面最大热流相对误差小于6%。