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。      

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     

水平变化双层波导声传播问题的耦合简正波解

为了验证现有模型的精度,导出了全反射下边界双层波导中简正波耦合矩阵的解析表达式,并将其应用到全局矩阵耦合简正波模型(Direct Global Matrix Coupled-Mode)中,使得该模型可以提供水平变化双层波导问题的标准解。文中首先利用COUPLE的简正波及耦合矩阵数值解验证了该简正波及耦合矩阵解析表达式的正确性;其次,采用改进的DGMCM模型求解了双层波导海山声传播损失,结果表明,改进后的DGMCM模型可以非常精确地求解水平变化双层波导问题,可作为求解此类问题的标准模型使用。     

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.     

A study on the multi-freedom broadband impedance model for time-domain simulations

The purpose of this paper is to construct a general broadband impedance model, which is suited for predicting acoustic propagation problems in time domain.A multi-freedom broadband impedance model for sound propagation over impedance surfaces is proposed and the corresponding time domain impedance boundary condition is presented.Basing on the extended Helmholtz resonator,the multi-freedom impedance model is constructed through combing with a sum of rational functions in the form of general complex-conjugate pole-residue pairs and it is proved that the impedance model is well posed.The impedance boundary condition can be implemented into a computational aeroacoustics solver by a recursive convolution technique, which results in a fast and computationally efficient algorithm.The two dimensional and three dimensional benchmark problems are selected to validate the accuracy of the proposed impedance model and time domain simulations.The numerical results are in good agreement with the reference solutions.It is demonstrated that the proposed impedance model can be used to describe the broadband characteristics of acoustic liners,and the corresponding time domain impedance boundary condition is viable and accurate for the prediction of sound propagation over broadband impedance surfaces.     

基于雷达海杂波的区域性非均匀蒸发波导反演方法

由于不同海域上空气象条件的不同, 海上蒸发波导在大尺度海面上空发生时通常是区域性非均匀的, 这一特性使得该环境中的电波传播特性相对于水平均匀的蒸发波导环境情况而明显不同, 因此, 进行区域性非均匀的蒸发波导探测反演对正确预测电波传播特性及提高雷达系统的工作性能具有重要的意义. 考虑到实际应用中蒸发波导信息获取手段的多样性, 将中尺度数值气象模式MM5预报的区域性蒸发波导修正折射率剖面作为先验信息, 提出了一种含该先验信息的区域性非均匀蒸发波导的雷达海杂波后验概率估计模型. 该模型使用主分量分析法对蒸发波导的水平非均匀性进行参数化建模, 然后通过贝叶斯理论将修正折射率剖面参数的先验概率分布、后验概率分布和似然函数联系起来, 利用雷达海杂波实现蒸发波导剖面参数的最大后验概率估计反演. 通过我国东海海域的实际区域性非均匀蒸发波导反演测试, 表明该模型能够以更高的精度实现区域性非均匀蒸发波导的反演.     

Solving the time-dependent Schrödinger equation by combining smooth exterior complex scaling and Arnoldi propagator

Abstract We develop a highly efficient scheme for numerically solving the three-dimensional time-dependent Schr?dinger equation of the single-active-electron atom in the field of laser pulses by combining smooth exterior complex scaling(SECS)absorbing method and Arnoldi propagation method.Such combination has not been reported in the literature.The proposed scheme is particularly useful in the applications involving long-time wave propagation.The SECS is a wonderful absorber,but its application results in a non-Hermitian Hamiltonian,invalidating propagators utilizing the Hermitian symmetry of the Hamiltonian.We demonstrate that the routine Arnoldi propagator can be modified to treat the non-Hermitian Hamiltonian.The efficiency of the proposed scheme is checked by tracking the time-dependent electron wave packet in the case of both weak extreme ultraviolet(XUV)and strong infrared(IR)laser pulses.Both perfect absorption and stable propagation are observed.     

一种水平变化波导中声传播问题的耦合模态法

针对介质参数及海底边界水平变化波导中的声传播问题,本文基于多模态导纳法提出一种能量守恒且便于数值稳定求解的耦合模态方法.将声压表示为一组正交完备的本地本征函数之和,对声压满足的Helmholtz方程在本地本征函数上作投影,推导出关于声压模态系数的二阶耦合模态方程组.耦合矩阵直观描述水平变化因素对模态耦合的贡献.为避免直接求解二阶耦合模态方程组可能遇到的数值发散问题,将其重构为两个耦合的一阶演化方程组,引入导纳矩阵并使用Magnus数值积分方法获得稳定的声场解.利用该耦合模态方法数值计算水平变化波导中的声场,并与COMSOL参考解比较,结果表明该耦合模态理论能够精确求解水平变化波导中的点源及分布源传播问题.     

Wave mode computing method using the step-split Padé parabolic equation

Models based on a parabolic equation (PE) can accurately predict sound propagation problems in range-dependent ocean waveguides. Consequently, this method has developed rapidly in recent years. Compared with normal mode theory, PE focuses on numerical calculation, which is difficult to use in the mode domain analysis of sound propagation, such as the calculation of mode phase velocity and group velocity. To broaden the capability of PE models in analyzing the underwater sound field, a wave mode calculation method based on PE is proposed in this study. Step-split Padé PE recursive matrix equations are combined to obtain a propagation matrix. Then, the eigenvalue decomposition technique is applied to the matrix to extract sound mode eigenvalues and eigenfunctions. Numerical experiments on some typical waveguides are performed to test the accuracy and flexibility of the new method. Discussions on different orders of Padé approximant demonstrate angle limitations in PE and the missing root problem is also discussed to prove the advantage of the new method. The PE mode method can be expanded in the future to solve smooth wave modes in ocean waveguides, including fluctuating boundaries and sound speed profiles.     

Propagation in a waveguide with range-dependent seabed properties

The ocean environment contains features affecting acoustic propagation that vary on a wide range of time and space scales. A significant body of work over recent decades has aimed at understanding the effects of water column spatial and temporal variability on acoustic propagation. Much less is understood about the impact of spatial variability of seabed properties on propagation, which is the focus of this study. Here, a simple, intuitive expression for propagation with range-dependent boundary properties and uniform water depth is derived. It is shown that incoherent range-dependent propagation depends upon the geometric mean of the seabed plane-wave reflection coefficient and the arithmetic mean of the cycle distance. Thus, only the spatial probability distributions (pdfs) of the sediment properties are required. Also, it is shown that the propagation over a range-dependent seabed tends to be controlled by the lossiest, not the hardest, sediments. Thus, range-dependence generally leads to higher propagation loss than would be expected, due for example to lossy sediment patches and/or nulls in the reflection coefficient. In a few instances, propagation over a range-dependent seabed can be calculated using range-independent sediment properties. The theory may be useful for other (non-oceanic) waveguides.     

Sound propagation in inhomogeneous waveguides with sound-speed profiles using the multimodal admittance method

The multimodal admittance method and its improvement are presented to deal with various aspects in underwater acoustics, mostly for the sound propagation in inhomogeneous waveguides with sound-speed profiles, arbitrary-shaped liquid-like scatterers, and range-dependent environments. In all cases, the propagation problem governed by the Helmholtz equation is transformed into initial value problems of two coupled first-order evolution equations with respect to the modal components of field quantities(sound pressure and its derivative), by projecting the Helmholtz equation on a constructed orthogonal and complete local basis. The admittance matrix, which is the modal representation of Direchlet-to-Neumann operator, is introduced to compute the first-order evolution equations with no numerical instability caused by evanescent modes. The fourth-order Magnus scheme is used for the numerical integration of differential equations in the numerical implementation. The numerical experiments of sound field in underwater inhomogeneous waveguides generated by point sources are performed. Besides, the numerical results computed by simulation software COMSOL Multiphysics are given to validate the correction of the multimodal admittance method. It is shown that the multimodal admittance method is an efficient and stable numerical method to solve the wave propagation problem in inhomogeneous underwater waveguides with sound-speed profiles, liquid-like scatterers, and range-dependent environments. The extension of the method to more complicated waveguides such as horizontally stratified waveguides is available.     

Finite difference split step method for non-paraxial semivectorial beam propagation in 3D

A non-paraxial semivectorial method in the finite difference split step scheme is proposed. The method can model wide-angle beam propagation in waveguides with high index contrast and gives good accuracy even for moderate discretization. A new method for splitting of operators is used to maintain the continuity of terms. This splitting also makes the propagation more efficient. The method is relatively insensitive to the choice of the reference refractive index.     

基于连续小波变换的简正波检测与提取技术

宽带声源在远距离传播中的频散过程反映着海洋环境特性的重要信息,准确提取这一过程中各简正波的有关信息是有效实现海洋声场反演的重要前提。小波变换虽然已被用于获取宽带声源的时频分布,但不具备适用于不同信号的柔性。在此背景下,本文介绍了一种自适应基小波方法,可适应不同形式的爆炸声信号,从而有效实现了频散现象的获取。在此基础上,本文同时建立了各号简正波的重构方法,经仿真测试,重构出的简正波与实际波形几乎相同。     

Waveguide invariant analysis for modeling time-frequency striations in a range-dependent environment

The waveguide invariant is a useful parameter for understanding the behavior of interference patterns (e.g., striations in time-frequency plots) resulting from broadband acoustic sources in shallow water waveguides. It is possible to model these striations for range-dependent environments using conventional parabolic equation methods; although this approach can be computationally intensive as a full field must be created for each frequency and azimuthally dependent geometry. This letter discusses the formulation and use of a range-dependent waveguide invariant distribution that can be used to describe spectral striation patterns using a fraction of the computing power required by parabolic equation methods.     

Benchmark solutions for sound propagation in an ideal wedge

Sound propagation in a wedge-shaped waveguide with perfectly reflecting boundaries is one of the few range-dependent problems with an analytical solution, and hence provides an ideal benchmark for a full two-way solution to the wave equation. An analytical solution for the sound propagation in an ideal wedge with a pressure-release bottom was presented by Buckingham and Tolstoy [Buckingham and Tolstoy 1990 J. Acoust. Soc. Am. 87 1511]. The ideal wedge problem with a rigid bottom is also of great importance in underwater acoustics. We present an analytical solution to the ideal wedge problem with a perfectly reflecting bottom, either rigid or pressure-release, which may be used to provide a means for investigating the sound field in depth-varying channels, and to establish the accuracy of numerical propagation models. Closed-form expressions for coupling matrices are also provided for the ideal waveguides characterized by a homogeneous water column bounded by perfectly reflecting boundaries. A comparison between the analytical solution and the numerical solution recently proposed by Luo et al. [Luo W Y, Yang C M and Zhang R H 2012 Chin. Phys. Lett. 29 014302] is also presented, through which the accuracy of this numerical model is illustrated.     

An Efficient Three-Dimensional Coupled Normal Mode Model and Its Application to Internal Solitary Wave Problems

We present an efficient three-dimensional coupled-mode model based on the Fourier synthesis technique. In principle, this model is a one-way model, and hence provides satisfactory accuracy for problems where the forward scattering dominates. At the same time, this model provides an efficiency gain of an order of magnitude or more over two-way coupled-mode models. This model can be applied to three-dimensional range-dependent problems with a slowly varying bathymetry or internal waves. A numerical example of the latter is demonstrated in this work. Comparisons of both accuracy and efficiency between the present model and a benchmark model are also provided.     

系统-热库模型平衡约化密度矩阵的精确计算:多层多构型含时Hartree方法及其与多电子态路径积分分子动力学方法的比较

An efficient and accurate method for computing the equilibrium reduced density matrix is presented for treating open quantum systems characterized by the system-bath model. The method employs the multilayer multiconfiguration time-dependent Hartree theory for imaginary time propagation and an importance sampling procedure for calculating the quantum mechanical trace. The method is applied to the spin-boson Hamiltonian, which leads to accurate results in agreement with those produced by the multi-electronic-state path integral molecular dynamics method.     

水平变化波导中两种耦合简正波方法的比较与分析

分析比较了处理水平变化波导中声传播问题的两种耦合简正波方法:DGMCM(Direct-Global-Matrix Coupled-Mode Method)和CCMM(Consistent Coupled-Mode Method)。首先,两种方法都提供声场的双向解,具有很高的计算精度。其次,DGMCM和CCMM中本地垂直模式序列均具有较快的收敛速度,但DGMCM比CCMM需要较少的水平分段数。再次,两种方法通过求解不同的耦合简正波系统得到声场解,但求解过程中所需参数的计算量基本相同。另外,DGMCM能够处理某些CCMM不容易解决的问题,如海底形状不平滑,线源在斜坡海底上方,以及多声源问题。在DGMCM方法中给出了双层波导问题的耦合矩阵解析表达式,还推导更新了CCMM模型,使其能够处理二维线源问题。      

海洋声学中三维抛物方程非均匀网格模型

在海洋声学中,三维抛物方程模型可以有效考虑三维空间的声传播效应。然而,采用三维抛物方程模型分析三维空间内的声传播问题时,计算时间较长,并且需要消耗较大的计算机内存,因此给远距离声场的快速精确计算带来了很大困难。为此,将非均匀网格Galerkin离散化方法用于三维直角坐标系下的水声抛物方程模型中,深度算子和水平算子Galerkin离散方式由均匀网格变为非均匀网格。仿真结果表明,三维直角坐标系下非均匀网格离散的抛物方程模型,在保持计算精度、提高计算速度的同时,可以实现远距离声场的快速预报。另外,针对远距离局部海底地形与距离有关的三维声传播问题,给出了声场快速计算方法;在海底保持水平的区域,采用经典Kraken模型,重构抛物方程算法的初始场,随后依次递推求解地形与距离有关海底下的三维声场。采用改进模型,证明了远距离楔形波导声强增强效应。      

Propagation in an elastic wedge using the virtual source technique

The virtual source technique, which is based on the boundary integral method, provides the means to impose boundary conditions on arbitrarily shaped boundaries by replacing them by a collection of sources whose amplitudes are determined from the boundary conditions. In this paper the virtual source technique is used to model propagation of waves in a range-dependent ocean overlying an elastic bottom with arbitrarily shaped ocean-bottom interface. The method is applied to propagation in an elastic Pekeris waveguide, an acoustic wedge, and an elastic wedge. In the case of propagation in an elastic Pekeris waveguide, the results agree very well with those obtained from the wavenumber integral technique, as they do with the solution of the parabolic equation (PE) technique in the case of propagation in an acoustic wedge. The results for propagation in an elastic wedge qualitatively agree with those obtained from an elastic PE solution.