耦合Galerkin简正波解的抛物方程方法水下声传播计算

研究水平变化的海洋环境下声传播的计算方法.把Galerkin方法的简正波解应用于耦合简正波抛物方程,可同时考虑海水和海底声场计算,对水平变化的海洋环境问题的数值计算表明,在包含海水和海底的声场计算中该方法的计算结果都具有较高的精度.     

解浅水方程的集中质量有限元方法

本文给出三角形单元集中质量有限元解浅水波方程的方法以及该方法在IBM-PC微机上的应用实例并取得较好结果。     

解Klein-Gordon方程的基于光滑分片Lagrange型插值的Galerkin方法

构造1种光滑的分片Lagrange型插值多项式空间,并在此空间中利用Galerkin法对非线性Klein-Gordon(NKG)方程进行求解.并分析数值格式的稳定性和收敛性,进行数值实验.数值结果表明格式精确有效.     

波群的波向线散开因子方程

本文将既适用于平面筒卡尔直角坐标系又适用于球面坐标系的基本式同文献(16)中的波向线方程结合，导出波群的波向线散开因子方程。由此方程解出的散开因子是波群组成波的波要素的函数。据此因子连同浅水系数和摩擦系数就可求得波群的波动强度或波高沿波向线的变化。在一定条件下，所导得的方程便分别化为形同于相应坐标系中单频率波的。所讨论的波群的折射是唯一地由水深变浅所致的。根据线性势论，得到由波数、波向和频率都彼此稍异的两系正弦波迭加而成的简单波群，海洋中的波群虽较这复杂得多，但两者本质上是相同的。故所提方程可作为计算浅水域中波群的折射系数的模式。     

浅水波能谱试验研究

室内试验是研究风浪特性的一重要途径,文中首先对试验研究方法中的不足进行了改进和探讨.对比了天然风浪与试验风浪的风场特点,确定了两者特征风速间的换算关系.通过采用人工风与不规则造波机相结合来生成与模拟风浪,延长了试验条件下风浪成长所需的风区长度.在此基础上,利用试验研究的优点,完成了较大范围浅水风浪试验,对浅水波能谱进行了深入探讨.研究表明,较深水情况波能谱在浅水域其谱峰变小,谱形变得更加尖窄,反映出其波能量趋于集中,并给出了相应的表达式.     

浅水波波高和周期的联合分布

用实验室资料研究变浅引起民的波高和周期联合分布的变化，资料取自两种海滩，实验资料与Ｌｏｎｇｕｅｔ－Ｈｉｇｇｉｎｓ提出的波主和周期的理论分布做了比较，对于ｄ／Ｌ〉０．１的非波碎波，观测和预报所和的分布形态吻合相当好，但由于Ｌｏｎｇｎｅｔ－Ｈｉｇｇｉｎｓ给出的预报的联合分布与预测的分布有位移，因此，提出了对观测位移的一种参数化法。另外还给出了谱宽度参数随汪水区域变化的一种参数化法。     

行经非平坦底面浅水孤立波演化的数值模拟

本文研究浅水孤立波行经非平坦底面的演化问题.将变底问题的Boussinesq方程进行改写后,直接应用三次样条理论离散,建立了一种简单且稳定的差分格式,对感兴趣的问题进行了多种数值模拟,对孤立波爬越过斜台阶后的分裂现象的数值结果与文献〔1—3〕的结果十分吻合,说明本文方法的可靠性.除此之外,本文对孤立波越过楔形以及孤立波形凸突底面的情况进行了多种参数的计算,显示出主波后逐渐衰弱的二次波列现象.     

孤立波爬坡的二维数值模拟

波浪在滩地上以及遇海岸工程后传播发生变形、爬坡等现象,对其进行数值模拟具有广阔的工程应用背景.应用基于Boltzmann方程的KFVS(kinetic flux vector splitting)格式求解二维浅水方程,同时采用干底Riemann解模拟动边界问题.模型模拟了孤立波在滩地上传播变形、爬坡的过程,以及孤立波在滩地上遇圆柱后绕射、变形和爬坡的过程.计算结果与实验结果非常吻合,表明模型具有较大的推广应用价值.     

浅水动力学的格子Boltzmann模拟

建立了一个格子Boltzmann模型,经过Chapman-Enskog展开可以恢复出守恒形式的浅水动力学方程组。理论分析和数值试验的结果都表明,本模型严格地满足质量守恒定律和动量定理。数值模拟了一维和二维溃坝流动,分别与理论解和文献值进行了对比,结果相当吻合。本模型具有很好的并行计算性能,在海洋、大气等大规模数值计算领域有着广阔的发展前景。     

An Explicit High Resolution Scheme for Nonlinear Shallow Water Equations

The present study develops a numerical model of the two-dimensional fully nonlinear shallow water equations （NSWE） for the wave run-up on a beach. The finite volume method （FVM） is used to solve the equations, and a second-order explicit scheme is developed to improve the computation efficiency. The numerical fluxes are obtained by the two dimensional Roe＇ s flux function to overcome the errors caused by the use of one dimensional fluxes in dimension splitting methods. The high-resolution Godunov-type TVD upwind scheme is employed and a second-order accuracy is achieved based on monotonic upstream schemes for conservation laws （MUSCL） variable extrapolation; a nonlinear limiter is applied to prevent unwanted spurious oscillation. A simple but efficient technique is adopted to deal with the moving shoreline boundary. The verification of the solution technique is carried out by comparing the model output with documented results and it shows that the solution technique is robust.     

Local discontinuous Galerkin method for far-field underwater explosion shock wave and cavitation

The shock wave and cavitation are main effects in the far-field underwater explosion, which could cause serious damage to marine structures. In this paper, the fluid mechanical behavior of blast load is described by the propagation of pressure wave. The acoustic pressure caused by far-field explosion is determined by solving the wave equation, where a strongly discontinuous axisymmetric numerical model is established with the local discontinuous Galerkin (LDG) method. The model can calculate the dynamic pressure in the fluid field and capture the high-resolution shock wave. The pressure cutoff model is employed to deal with the cavitation effect due to the reflection of the shock wave. The numerical model is verified by comparing with the analytical solution of the cavitation effect near the structure in one dimension. With the same mesh discretization, the present model shows higher precision than the results calculated by the acoustic finite element method. In addition, the propagation of shock wave in the cylindrical water column is studied. Finally, the formation, growth and collapse of the cavitation region near the free surface are simulated. The LDG model can remove the spurious oscillations behind the shock front and it’s more accurate than the results of the acoustic finite element method, in terms of capturing the sharpness of shock wave and calculating the shock and cavitation loading. And the present model can be applied to calculate the structural damage caused by shock wave in three dimensions.     

VHR Marine 3D Seismics for Shallow Water Investigations: Some Practical Guidelines

The design of very high resolution (VHR) 3D marine surveys not only depends on the theoretical considerations of seismic imaging, but is also dictated by the field conditions and the available budget. The main geophysical controlling factors include the depth and dip of the target, and horizontal and vertical resolution. Working in shallow water environments and at high frequencies will imply constraints on sampling, array directivity and positioning accuracy. In this paper we describe the main requirements and constraints involved in VHR 3D acquisition. The second part of the paper focuses on the flexible acquisition system “Opus3D” recently developed for shallow water investigations. The system provides improvements in imaging resolution in a relatively simple and cost-effective way. Acquisition and positioning constraints limit the system to nearshore studies. The experience gained from various surveys with this new acquisition system allow us to formulate a number of practical specifications and guidelines for 3D survey design in shallow water.     

变浅作用下浅水海浪谱的计算

深水海浪向近岸传播过程中,由于变浅作用,其波面高度分布,波谱都发生了变化。本文基于非线性系统的输出和输入间亦存在转换关系,通过波面高度分布函数建立了深水正态海浪过程作为输入和浅水偏态海浪过程作为输出之间的非线性转换关系,导出了深、浅水谱间的理论关系。在假定能通量不变的条件下,提出了一种由已知深水谱和波面偏度计算二维海浪变浅作用下的浅水谱的方法,并对其进行了讨论和检验。     

Wave Numerical Model for Shallow Water

The history of forecasting wind waves by wave energy conservation equation is briefly des-cribed.Several currently used wave numerical models for shallow water based on different wave theoriesare discussed.Wave energy conservation models for the simulation of shallow water waves are introduced,with emphasis placed on the SWAN model,which takes use of the most advanced wave research achieve-ments and has been applied to several theoretical and field conditions.The characteristics and applicabilityof the model,the finite difference numerical scheme of the action balance equation and its source termscomputing methods are described in detail.The model has been verified with the propagation refractionnumerical experiments for waves propagating in following and opposing currents;finally.the model is ap-plied to the Haian Gulf area to simulate the wave height and wave period field there,and the results arecompared with observed data.     

The Boomer Sound Source as a Tool for Shallow Water Geophysical Exploration

Technical specifications for small seismic sound sources used in seismic profilers may provide details of the pressure signatures as measured on the primary acoustic axis and in the far field but will rarely provide information regarding off-axis emission or of the form of the signatures in the near field. Since shallow water geophysical mapping is now attracting more attention in research establishments and in the commercial sector, off-axis information could become an important issue. The use of a wide angle seismic configuration on a small scale will demand that directional source information be included in data processing activities if the full potential of the data is to be realised. Direct measurement of the full near and far field characteristics of a source are often not practical, however modelling of the acoustic field may offer a tractable alternative and a means of rapidly generating source functions appropriate for advanced data processing. One such modelling approach reviewed here uses a time domain method to synthesise off-axis signatures using a far field, on-axis reference signature.     

The Nonlinear Wave Force on a Circular Cylinder in Shallow Water

Based on the 1st order cnoidal wave theory, the nonlinear wave diffraction around a circular cylinder in shallow water is studied in this paper. The equation of the wave surface around the cylinder is formulated and by using this formula the wave surface elevation on the cylinder surface can be obtained. In this paper, the formula for calculating the cnoidal wave force on a circular cylinder is also derived. For the wave conditions which are often encountered in practical engineering designs, the ratios of the nonlinear wave forces to the linear wave forces are calculated, and the results are plotted in this paper for design purposes. In order to verify the theoretical results, model tests are conducted. After comparing the test results with the theoretical ones, it is concluded that, in shallow water, for the case of T g / d~(1/2) > 8-10 and H / d > 0.3, the cnoidal wave theory should be used to calculate the wave action on a cylindrical pier.     

Transformation of Wave Energy Spectrum in Shallow Water

- Combined with irregular wave-maker, the growing process of Wave Energy Spectrum in shallow water can be studied in wind wave channel on different water depth conditions, and its transformation characteristics and rules can be obtained.     

基于间断有限元方法的三维近岸波生流数值模型建立

在三维水动力模型中引入三维辐射应力,水滚影响以及波浪附加紊动效应,并基于间断有限元方法建立了非结构化网格三维波生流数值模型。采用实验室内斜坡地形条件下正向入射波在破波带附近产生的近底回流和斜向入射波产生的沿岸流对模型进行了验证。结果表明,计算值与实测值吻合程度较好,该模型可以较好地描述三维近岸波生流。     

Nonlinear Wave Force on Pier Group in Shallow Water

Based on the 1st order cnoidal wave theory, the wave diffraction around the pier group inshallow water is studied in this paper. The formulas for calculating the nonlinear wave forces are also presented here. In order to verify the theoretical results, model tests are conducted in the wave flume in The State Key Laboratory of Coastal and Offshore Engineering located in Dalian University of Technology. The range of the wave parameters in the experiments is characteristic wave period T g/d~(1/2) = 8.08- 22.86, characteristic wave height H/ d= 0.1 ~ 0.45. The results obtained from the experiments agree with the theoretical results quite well. It is shown that, in shallow water the nonlinear wave forces acting on a pier group are greater than those calculated by linear wave theory, the value of increment in wave force increases with the increases of the nonlinearity of the wave. In the wave range studied in this paper, the nonlinear wave force can reach over 4 times the force calculatecd by linear wave theory. Thus, it is suggested that, when Tg / d~(1/2)> 8, the wave force on the piers in the pier group in shallow water should be calculated by using the cnoidal wave theory.