A two-way marching coupled-mode method for range-dependent propagation

##正##An efficient,accurate,and numerically stable coupled-mode solution is presented for acoustic propagation in a range-dependent waveguide.This method is numerically stable due to the appropriately normalized range solutions introduced in the formulation.In addition,by combining a forward marching and a backward marching,this method provides accurate solutions for range-dependent propagation problems,especially those characterized by large bottom slope angle and/or high impedance contrast between water and the bottom.Furthermore,this two-way solution also provides high efficiency,which is achieved by applying the single-scatter approximation.Numerical examples are also provided to demonstrate the efficiency,accuracy, and stability of this method.     

全局矩阵耦合简正波方法与现有模型的比较

水平变化波导中的全局矩阵耦合简正波方法具有数值稳定、计算精度高、计算效率高、适用范围广等优点。骆文于等人开发了全局矩阵耦合简正波模型DGMCM (Luo et al, "A numerically stable coupled-mode formulation for acoustic propagation in range-dependent waveguides," Sci.China-Phys.Mech.Astron.55,572(2012))。与现有耦合简正波模型COUPLE相比,DGMCM模型主要有如下改进:无条件稳定;适用范围更广;计算效率更高。DGMCM模型具有与COUPLE模型同等的计算精度,均能提供声场的完全双向解,两者在计算精度方面均优于基于抛物方程理论的单向声传播模型RAM。本文从理论上分析DGMCM模型与现有模型COUPLE和RAM的差异,并利用数值算例加以验证。      

A three-dimensional coupled-mode model for the acoustic field in a two-dimensional waveguide with perfectly reflecting boundaries

This paper presents a three-dimensional(3D) coupled-mode model using the direct-global-matrix technique as well as Fourier synthesis. This model is a full wave, two-way three-dimensional model, and is therefore capable of providing accurate acoustic field solutions. Because the problem of sound propagation excited by a point source in an ideal wedge with perfectly reflecting boundaries is one of a few three-dimensional problems with analytical solutions, the ideal wedge problem is chosen in this work to validate the presented three-dimensional model. Numerical results show that the field results by analytical solutions and those by the presented model are in excellent agreement, indicating that the presented model can serve as a benchmark model for three-dimensional sound propagation problems involving a planar two-dimensional geometry as well as a point source.     

An efficient broadband coupled-mode model using the Hamiltonian method for modal solutions

A numerically efficient broadband, range-dependent propagation model is proposed, which incorporates the Hamiltonian method into the coupled-mode model DGMCM. The Hamiltonian method is highly efficient for finding broadband eigenvalues, and DGMCM is an accurate model for range-dependent propagation in the frequency domain. Consequently, the proposed broadband model combining the Hamiltonian method and DGMCM has significant virtue in terms of both efficiency and accuracy. Numerical simulations are also provided. The numerical results indicate that the proposed model has a better performance over the broadband model using the Fourier synthesis and COUPLE, while retaining the same level of accuracy.     

水平变化波导中的全局矩阵耦合简正波方法

提出了一种新的水平变化波导中声场的耦合简正波求解方法,该方法能够处理二维点源和线源问题,提供声场的双向解。该方法利用全局矩阵(DGM)一次性求解耦合模式的系数,消除了传播矩阵递推求解中存在的误差累积问题;此外,改善了现有模型中对距离函数的归一化方法,从而避免了泄露模式指数增长导致的数值溢出问题。本文还给出了绝对软海底理想波导中耦合矩阵的闭合表达式,并分析了单个阶梯下简正波耦合现象。此外,本文还计算了理想楔形波导中的声传播问题(ASA标准问题),并与解析解及COUPLE07计算结果进行了比较,结果表明该方法是一种稳定、精确的水平变化波导中的声场计算方法。      

Acoustic scattering by arbitrary distributions of disjoint, homogeneous cylinders or spheres

A T-matrix formulation is presented to compute acoustic scattering from arbitrary, disjoint distributions of cylinders or spheres, each with arbitrary, uniform acoustic properties. The generalized approach exploits the similarities in these scattering problems to present a single system of equations that is easily specialized to cylindrical or spherical scatterers. By employing field expansions based on orthogonal harmonic functions, continuity of pressure and normal particle velocity are directly enforced at each scatterer using diagonal, analytic expressions to eliminate the need for integral equations. The effect of a cylinder or sphere that encloses all other scatterers is simulated with an outer iterative procedure that decouples the inner-object solution from the effect of the enclosing object to improve computational efficiency when interactions among the interior objects are significant. Numerical results establish the validity and efficiency of the outer iteration procedure for nested objects. Two- and three-dimensional methods that employ this outer iteration are used to measure and characterize the accuracy of two-dimensional approximations to three-dimensional scattering of elevation-focused beams.     

太赫兹金属线波导耦合模理论研究(英文)

基于耦合模假设,研究了描述两太赫兹金属线波导之间耦合特性的耦合模理论.通过采用与光波导耦合模理论等价的近似,研究得到了耦合方程和耦合系数表达式.进而,研究得到了两个相同金属线波导的耦合方程解及耦合特性.所提出的理论对于描述两金属线波导之间的能量传递具有重要的意义.     

基于弱耦合模理论的空间多波导耦合特性研究

不在同一平面的空间多波导中光耦合发生在横截面两个方向,利用空间多波导可以方便、有效地实现不同层间器件的互连。将平面波导耦合模理论推广到空间多波导之间的耦合,在弱导引条件下给出了空间多波导的耦合方程。利用该耦合方程对三维集成光学器件中常见的空间三波导和空间四波导的耦合特性进行分析,得出光强分布及耦合长度的解析表达式,并用三维全矢量光束传输法验证了分析结果。分析结果表明利用空间多波导可以实现水平和垂直两个方向上的均匀或非均匀分束,为利用空间多波导之间相互耦合的三维定向耦合器件的设计和分析提供理论基础。     

Three-dimensional coupled-mode model and characteristics of low-frequency sound propagation in ocean waveguide with seamount topography

Large-scale topography, such as a seamount, substantially impacts low-frequency sound propagation in an ocean waveguide, limiting the application of low-frequency acoustic detecting techniques. A three-dimensional (3D) coupled-mode model is developed to calculate the acoustic field in an ocean waveguide with seamount topography and analyze the 3D effect. In this model, a correction is introduced in the bottom boundary, theoretically making the acoustic field satisfy the energy conservation. Furthermore, a large azimuth angle calculation range is obtained by using the operator theory and higher-order Padé approximation. Additionally, the model has advantages related to the coupling mode and parabolic equation theory. The couplings corresponding to the effects of range-dependent environment are fully considered, and the numerical implementation is kept feasible. After verifying the accuracy and reliability of the model, low-frequency sound propagation characteristics in the seamount environment are analyzed. The results indicate lateral variability in bathymetry can lead to out-of-plane effects such as the horizontal refraction phenomenon, while the coupling effect tends to restore the abnormal sound field and produces acoustic field diffraction behind the seamount. This model effectively considers the effects of the horizontal refraction and coupling, which are proportional to the scale of the seamount.     

Coupled-mode solutions in generalized ocean environments

This paper presents the application of the differential equation approach to solving the second-order coupled-mode equations in inhomogeneous ocean environments. The model incorporates sound velocity profile points to construct depth-dependent, piecewise linear, ocean and bottom environments along a range grid. Modal solutions are evaluated in terms of Airy functions. The formalism to evaluate analytically the mode-coupling coefficients is presented. Comparisons to conventional expressions of the coefficients are made. The integro-differential form of the coupled equations is solved using an approach developed in nuclear theory that incorporates the Lanczos method [Knobles, J. Acoust. Soc. Am. 96, 1741-1747 (1994)]. Demonstration of the practicality of this approach is made by applying the results in actual calculations with realistic ocean environments. The formalism to evaluate analytically the mode-coupling coefficients is presented. Several benchmark examples were examined in order to validate the model and are discussed, including propagation over a hill, benchmark wedge problems, and a range-varying sound speed profile benchmark. The importance of this model is also demonstrated by the physical insight gained in having a coupled-mode approach to solving range-dependent problems.     

A model for sonar interrogation of complex bottom and surface targets in shallow-water waveguides

Many problems of current interest in underwater acoustics involve low-frequency broadband sonar interrogation of objects near the sea surface or sea floor of a shallow-water environment. When the target is situated near the upper or lower boundary of the water column the acoustic interactions with the target objects are complicated by interactions with the nearby free surface or fluid-sediment interface, respectively. A practical numerical method to address such situations is presented. The model provides high levels of accuracy with the flexibility to handle complex, three-dimensional targets in range-independent environments. The model is demonstrated using several bottom target scenarios, with and without locally undulating seabeds. The impact of interface and boundary interactions is considered with an eye toward using the sonar return signal as the basis for acoustic imaging or spectral classification.     

时域耦合模理论引入“理论力学”教学中的可行性的探究

被广泛地用于力学、光学、电学等相关学科中的时域耦合模理论,在前沿科学研究中扮演着越来越重要的角色.在教学和科研相结合的本科教学理念下,将时域耦合模理论引入“理论力学”中已刻不容缓.本文结合拉格朗日方程和久期微扰理论,将振子耦合的二阶微分方程退化为一阶微分方程,即时域耦合模理论的主方程.该探究为本科生顺利接受时域耦合模理论提供了一种方案,并且在本科生素质培养方面有一定的意义.     

一种水平变化可穿透波导中声传播问题的耦合简正波方法

通过利用标准简正波程序KRAKEN计算本地简正波解及耦合矩阵, 进一步发展了求解水平变化波导中声场的全局矩阵耦合简正波方法(Luo et al., "A numerically stable coupled-mode formulation for acoustic propagation in range-dependent waveguides," Sci. China-Phys. Mech. Astron. 55, 572 (2012)), 使得该方法可以处理具有可穿透海底及随深度变化声速剖面等实际问题, 并提供声场的完全双向解. 本文还给出了双层波导中耦合矩阵的解析表达式, 并利用其验证了本方法中耦合矩阵数值算法的精度. 最后, 利用改善后的全局矩阵耦合简正波模型(DGMCM)计算了美国声学学会(ASA)提出的可穿透楔形波导标准问题, 将所得数值解与参考解比较, 结果表明DGMCM方法可以精确处理水平变化波导中声传播实际问题. 关键词： 耦合简正波理论 全局矩阵方法 可穿透楔形波导     

A fast and precise three-dimensional measurement system based on multiple parallel line lasers

This paper conducts a trade-off between efficiency and accuracy of three-dimensional(3 D)shape measurement based on the triangulation principle,and introduces a flying and precise 3 D shape measurement method based on multiple parallel line lasers.Firstly,we establish the measurement model of the multiple parallel line lasers system,and introduce the concept that multiple base planes can help to deduce the unified formula of the measurement system and are used in simplifying the process of the calibration.Then,the constraint of the line spatial frequency,which maximizes the measurement efficiency while ensuring accuracy,is determined according to the height distribution of the object.Secondly,the simulation analyzing the variation of the systemic resolution quantitatively under the circumstance of a set of specific parameters is performed,which provides a fundamental thesis for option of the four system parameters.Thirdly,for the application of the precision measurement in the industrial field,additional profiles are acquired to improve the lateral resolution by applying a motor to scan the 3 D surface.Finally,compared with the line laser,the experimental study shows that the present method of obtaining 41220 points per frame improves the measurement efficiency.Furthermore,the accuracy and the process of the calibration are advanced in comparison with the existing multiple-line laser and the structured light makes an accuracy better than 0.22 mm at a distance of 956.02 mm.     

矩形表面波探头声场的高斯声束叠加法

利用矩形压电晶片和有机玻璃楔块折射可激励出超声表面波,广泛用于固体近表面缺陷检测和材料特性测量.由于描述表面波三维声场的理论方法还鲜有报道,因而主要采用简化的表面波二维声场模型来定量分析这类问题.高斯声束模型近些年被广泛应用于解决超声体波传播的各种复杂问题,然而,目前还没有将其扩展应用到超声表面波的声场的计算中.通过结合表面波格林方程和矩形换能器的高斯声束模型,推导出基于高斯声束叠加的表面波三维声场解析解.进一步,将该方法与点源叠加的数值解进行了分析比较,计算结果表明表面波声场的高斯声束叠加方法在具有较好计算精度的同时,还具有更快的计算效率.     

应用分离涡模型计算斜圆柱孔气膜冷却

分离涡模型(DES,Detached eddy simulation)兼有雷诺时均湍流模型计算量较小和大涡模拟计算精度高的优点。本文利用DES对平板单斜圆柱孔的气膜冷却进行了数值模拟,并将结果同RANS湍流模型的计算结果以及实验数据相比较,表明DES能有效弥补RANS湍流模型在计算三维不均匀非定常湍流场的不足,更接近实际地反映了气膜冷却中的流动和换热的本质规律。     

A mass-conserved multiphase lattice Boltzmann method based on high-order difference

The Z–S–C multiphase lattice Boltzmann model [Zheng, Shu, and Chew(ZSC), J. Comput. Phys. 218, 353(2006)]is favored due to its good stability, high efficiency, and large density ratio. However, in terms of mass conservation, this model is not satisfactory during the simulation computations. In this paper, a mass correction is introduced into the ZSC model to make up the mass leakage, while a high-order difference is used to calculate the gradient of the order parameter to improve the accuracy. To verify the improved model, several three-dimensional multiphase flow simulations are carried out,including a bubble in a stationary flow, the merging of two bubbles, and the bubble rising under buoyancy. The numerical simulations show that the results from the present model are in good agreement with those from previous experiments and simulations. The present model not only retains the good properties of the original ZSC model, but also achieves the mass conservation and higher accuracy.     

Coupled-Mode Analysis of an NRD-Guide Coupler Based on Singular Perturbation Technique

A coupled-mode formulation for an NRD-guide coupler is presented using the singular perturbation technique. The first-order and second-order perturbations are taken into account in the analysis and the coupled-mode equations based on the eigenmodes of each waveguide in isolation are derived. The propagation constants obtained by these equations are compared with those by the exact theory, conventional coupled-mode theory, and improved coupled-mode theory. The numerical results of present formulation are in good agreement with the exact theory and superior to those of the other formulations.     

Coupled-mode approach to surface plasmon polaritons in nonlinear periodic structures

We present a coupled-mode theory describing light propagation in an array of nonlinear plasmonic waveguides. Our model predicts a two-band dependence of the propagation constant versus transverse quasi-momentum and existence of discrete and gap plasmon solitons.     

Lattice Boltzmann method for three-dimensional moving particles in a Newtonian fluid

A lattice Boltzmann method is developed to simulate three-dimensional solid particle motions in fluids. In the present model, a uniform grid is used and the exact spatial location of the physical boundary of the suspended particles is determined using an interpolation scheme. The numerical accuracy and efficiency of the proposed lattice Boltzmann method is demonstrated by simulating the sedimentation of a single sphere in a square cylinder. Highly accurate simulation results can be achieved with few meshes, compared with the previous lattice Boltzmann methods. The present method is expected to find applications on the flow systems with moving boundaries, such as the blood flow in distensible vessels, the particle－flow interaction and the solidification of alloys.