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.

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.

An analytical study on the Rayleigh wave generation in a stratified structure

In this paper,an analytical method is used to investigate the Rayleigh wave generation in a stratified structure and the wave generation in a dry sandy layer constrained between the couple stress and inhomogeneous orthotropic half-spaces.This study is devoted to analyzing the impact of various effective parameters associated with the media on the phase velocities of the wave.The displacement components for each medium are derived by implementing the separable variable method.The frequency equa-tion is secured by using the displacement components in the boundary conditions,imposed at the interfaces between the layer and half-spaces.Moreover,the secured equation is the relation between the phase velocity and the wave number.Numerical computations are performed,and graphical representations are demonstrated between the phase velocity and the wave number for both phase velocities with different values of the parameters.The comparison between the phase velocities is observed for the same value of each pa-rameter.

A General Linear Wave Theory for Water Waves Propagating over Uneven Porous Bottoms

Starting from the widespread phenomena of porous bottoms in the near shore region, considering fully the diversity of bottom topography and wave number variation, and including the effect of evanescent modes, a general linear wave theory for water waves propagating over uneven porous bottoms in the near shore region is established by use of Green's second identity. This theory can be reduced to a number of the most typical mild-slope equations currently in use and provide a reliable research basis for follow-up development of nonlinear water wave theory involving porous bottoms.

Refraction-Diffraction Mathematical Model for Waves With Lateral Energy Transmission Mechanism and Its Verification

To solve problems concerning wave elements and wave propagation, an effective way is the wave energy balance equation, which is widely applied in oceanography and ocean dynamics for its simple computation. The present papaer advances wave energy balance equations considering lateral energy transmission and energy loss as the governing equation for the study of wave refraction-diffraction. For the mathematical model, numerical simulation is made by means of difference method, and the result is verified with two examples.

Explicit Solution to the Wave Dispersion Equation with Higher Accuracy

Based on the previous study results, two higher accuracy explicit solutions to the dispersion equation for wave length are presented in this paper. These two solutions have an accuracy of 0. 1% over all wave lengths, which is sufficiently complete for practical application. At the same time, several previous explicit solutions also have been reviewed and compared herein. In comparison with accuracy, the results show that the present two solutions are as good as Wu and Thornton＇s solution （which has a good accuracy over all wave lengths, but its calculation formula is so complex that it is hard to be used with a hand calculator）, and are better than the other solutions, they may be rather useful in practical calculation with a hand calculator or computer.

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.

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.

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.

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.

Structure of Periodic Flows through a Channel with a Suddenly Expanded and Contracted Part

With respect to flows in a two-dimensional sudden expansion and contraction channel having a pair of cavities, numerical simulation was performed by imposing inlet/outlet boundary conditions giving a velocity distribution to the inlet. Periodic flows have been reproduced, which have a discrete spectrum about frequency. A fundamental wave occupies most part of the disturbance components, but higher harmonic waves are also included. The disturbance is excited by Kelvin-Helmholtz instability in a cavity section, where only the fundamental wave is generated. A wavenumber is regulated by a channel length under a periodic boundary condition, but there is no restriction in a main flow direction under the inlet/outlet boundary conditions, and therefore, some wavenumbers can occur. Therefore, an arbitrary frequency component of disturbance is a synthesized wave composed of various wave numbers. There are two kinds of components constituting this synthesized wave: a maximum of a velocity distribution is near a wall and in the center of the channel, which are called as wall mode and central mode in linear stability analysis of the plane Poiseuille flow. The synthesized wave composed of some modes shows a tendency to lower wavenumbers at the center of the channel.

Analysis of ground vibrations due to underground trains by 2.5D finite/infinite element approach

The 2.5D finite/infinite element approach is adopted to study wave propagation problems caused by underground moving trains. The irregularities of the near field, including the tunnel structure and parts of the soil, are modeled by the finite elements, and the wave propagation properties of the far field extending to infinity are modeled by the infinite elements. One particular feature of the 2.5D approach is that it enables the computation of the three-dimensional response of the half-space, taking into account the load-moving effect, using only a two-dimensional profile. Although the 2.5D finite/infinite element approach shows a great advantage in studying the wave propagation caused by moving trains, attention should be given to the calculation aspects, such as the rules for mesh establishment, in order to avoid producing inaccurate or erroneous results. In this paper, some essential points for consideration in analysis are highlighted, along with techniques to enhance the speed of the calculations. All these observations should prove useful in making the 2.5D finite/infinite element approach an effective one.

Kinematics Modeling and Experiments of Pectoral Oscillation Propulsion Robotic Fish

A robotic fish driven by oscillating fins, 'Cownose Ray-I', is developed, which is in dorsoventrally flattened shape without a tail. The robotic fish is composed of a body and two lateral fins. A three-factor kinematic model is established and used in the design of a mechanism. By controlling the three kinematic parameters, the robotic fish can accelerate and maneuver. Forward velocity is dependent on the largest amplitude and the number of waves in the fins, while the relative contribution of fin beat frequency to the forward velocity of the robotic fish is different from the usual result. On the other hand, experimental results on maneuvering show that phase difference has a stronger effect on swerving than the largest amplitude to some extent. In addition, as propulsion waves pass from the trailing edge to the leading edge, the robotic fish attains a backward velocity of 0. 15 m·s^(-1).

A time-dependent numerical model of the mild-slope equation

On the basis of the previous studies, the simplest hyperbolic mild-slope equation has been gained and the linear time - dependent numerical model for the water wave propagation has been established combined with different boundary conditions. Through computing the effective surface displacement and transforming into the real transient wave motion, related wave factors will be calculated. Compared with Lin＇s model, analysis shows that calculation stability of the present model is enhanced efficiently, because the truncation errors of this model are only contributed by the dissipation terms, but those of Lin＇s model are induced by the convection terms, dissipation terms and source terms. The tests show that the present model succeeds the merit in Lin＇ s model and the computational program is simpler, the computational time is shorter, and the computational stability is enhanced efficiently. The present model has the capability of simulating transient wave motion by correctly predicting at the speed of wave propagation, which is important for the real - time forecast of the arrival time of surface waves generated in the deep sea. The model is validated against analytical solution for wave diffraction and experimental data for combined wave refraction and diffraction over a submerged elliptic shoal on a slope. Good agreements are obtained. The model can be applied to the theory research an d engineering applications about the wave propagation in a biggish area.

Giant Magnetostrictive Material Loudspeaker System Acoustic Radiation Simulation

An infinite panel model of giant magnetostrictive material loudspeaker system （GMMLS） is proposed by making use of finite element method（FEM）. Bending wave eigenfunction is introduced to describe the acoustic radiation condition of the panel. Far-field response in different conditions is calculated by changing the mass surface density. Conclusion is obtained by analyzing the curves simulated, that panel which has larger mass surface density can hardly generate far-field acoustic radiation for lower frequency, while the panel has smaller mass surface density generates far-field acoustic radiation for lower frequency evenly and stronger.

Infinite Sequence of Conservation Laws and Analytic Solutions for a Generalized Variable-Coefficient Fifth-Order Korteweg-de Vries Equation in Fluids

In this paper, an infinite sequence of conservation laws for a generalized variable-coefficient fifth-order Korteweg-de Vries equation in fluids are constructed based on the Backlund transformation. Hirota bilinear form and symbolic computation are applied to obtain three kinds of solutions. Variable coefficients can affect the conserved density, associated flux, and appearance of the characteristic lines. Effects of the wave number on the soliton structures are also discussed and types of soliton structures, e.g., the double-periodic soliton, parallel soliton and soliton complexes, are presented.

A Meshless Collocation Method with Barycentric Lagrange Interpolation for Solving the Helmholtz Equation

In this paper,Chebyshev interpolation nodes and barycentric Lagrange interpolation basis function are used to deduce the scheme for solving the Helmholtz equation.First of all,the interpolation basis function is applied to treat the spatial variables and their partial derivatives,and the collocation method for solving the second order differential equations is established.Secondly,the differential matrix is used to simplify the given differential equations on a given test node.Finally,based on three kinds of test nodes,numerical experiments show that the present scheme can not only calculate the high wave numbers problems,but also calculate the variable wave numbers problems.In addition,the algorithm has the advantages of high calculation accuracy,good numerical stability and less time consuming.

Ray Tracing for Doppler Backscattering System in the Experimental Advanced Superconducting Tokamak

The Doppler backscattering system has been widely used for turbulence measurements,and the microwave beam will be backscattered near the cut-off layer when the Brag condition is fulfilled.In tokamak,the ray-tracing code is used to obtain the radial position and perpendicular wave number of the scattering layer for turbulence velocity measurement and the WKB（Wentzel-Kramers-Brillouin） approximation should be satisfied for optical propagation.To calculate the backscattering location and wave number at the cut-off layer only,a single ray tracing in the cross section is enough,while for spatial and wave number resolution calculation,multiple rays reflecting the microwave beam size should be used.Considering the angle between the wave vector and the magnetic field,a three-dimension quasi-optical Gaussian ray tracing is sometimes needed.

WIDE SWATH FMCW SAR DATA PROCESSING IN SQUINT MODE

This paper concentrates on the data processing of Frequency Modulation Continuous Wave(FMCW),Synthetic Aperture Radar(SAR)in the case of wide swath and squint mode.In the mode,the Doppler centroid dramatically varies along slant range compared to conventional pulsed-SAR.This poses a challenge for system design and signal processing since a very large azimuth bandwidth would be introduced.In the paper,we accommodate the Doppler centroid variations with range by an improved spectral-length extension method,where a bulk range shift and updated Doppler centroid variations are introduced to greatly reduce the azimuth aliasing with respective to the existing methods.Moreover,an image formation approach that integrates wave number domain algorithm is presented to focus the raw data of FMCW SAR in the case of wide swath and squint mode.Point target simulation experiment demonstrates the advantages of the presented method.