具有精确色散性的非线性波浪数学模型

以完全非线性的自由表面边界条件为基础,以波面升高\eta和自由表面速度势\phi _\eta为待求变量,建立了新的波浪方程．方程在色散性上是完全精确的,非线性近似至三阶．与缓坡方程相比较,两者都具有精确的色散性,但该方程属于非线性模型,可模拟波浪的非线性效应,且适用于不规则波．方程的特点是属于微分-积分方程,对如何处理方程中积分项进行了讨论,并数值模拟了不同周期的线性波和二阶Stokes波,也模拟了波群的非线性演化,以对模型进行验证．      

THE DIRECTION DEPENDENCE OF SURFACE WAVE SPEED AT THE SURFACE OF MAGNETO-ELECTRO-ELASTIC HALF-SPACE

The direction dependence of surface wave speed and the influence of electrically and magnetically short/open circuit are investigated in this paper. First, the elastic, piezoelectric and piezomagnetic coefficients in the considered ordinate system are obtained by Bonde transformation from those in the crystal axis ordinate system. Then, the secular equation of surface wave is derived from the free traction condition on the surface of half space with consideration of short/open circuit case. Some numerical examples are given. The direction dependence of surface wave speed and the influences of short/open circuit are shown graphically and discussed based on the numerical results.     

A Computational Method for Free-Surface Viscous Flows Through Porous Media

In this paper we have investigated free-surface unsteady viscous flow through porous media using a finite difference technique via primitive formulation. A transformation has been used to convert the irregular flow domain into a rectangular domain. Two illustrations have been presented in case of a standing wave problem and a cavity flow problem with a free surface. The method is found satisfactory for numerical solution for Reynolds number upto 200.     

Numerical simulations of inviscid and viscous free‐surface flows with application to nonlinear water waves

The purpose of the present study is to establish a numerical model appropriate for solving inviscid/viscous free‐surface flows related to nonlinear water wave propagation. The viscous model presented herein is based on the Navier–Stokes equations, and the free‐surface is calculated through an arbitrary Lagrangian–Eulerian streamfunction‐vorticity formulation. The streamfunction field is governed by the Poisson equation, and the vorticity is obtained on the basis of the vorticity transport equation. For computing the inviscid flow the Laplace streamfunction equation is used. These equations together with the respective (appropriate) fully nonlinear free‐surface boundary conditions are solved using a finite difference method. To demonstrate the model feasibility, in the present study we first simulate collision processes of two solitary waves of different amplitudes, and compute the phenomenon of overtaking of such solitary waves. The developed model is subsequently applied to calculate (both inviscid and the viscous) flow field, as induced by passing of a solitary wave over submerged rectangular structures and rigid ripple beds. Our study provides a reasonably good understanding of the behavior of (inviscid/viscous) free‐surface flows, within the framework of streamfunction‐vorticity formulation. The successful simulation of the above‐mentioned test cases seems to suggest that the arbitrary Lagrangian–Eulerian/streamfunction‐vorticity formulation is a potentially powerful approach, capable of effectively solving the fully nonlinear inviscid/viscous free‐surface flow interactions. Copyright © 2009 John Wiley & Sons, Ltd.     

滚波演化中聚合过程的数值模拟研究

滚波是一种重力作用下自由液面失稳诱发的水面波动现象, 通常可分为具有相对稳定波形和波速的周期性滚波与波形和波速不断变化的不规则滚波(自然滚波). 不规则滚波的相互作用和发展演化过程十分复杂, 至今对其认识尚不成熟. 本文采用基于雷诺平均Navier-Stokes方程的立面二维数值模型, 对不规则滚波发展过程中的吸收聚合和追赶聚合现象进行了数值模拟研究. 分析了两种聚合模式的演化过程, 给出了滚波聚合过程中完整的波形、波速、速度剖面以及湍流黏性等重要信息. 结果表明滚波的聚合过程是不规则滚波演化和增长的重要机制, 在特定条件下滚波增长由自然增长模式转变为以吸收聚合和追赶聚合为主的增长模式. 滚波聚合过程中, 依次经历后波追赶、爬升、与前波合并、内部流场调制等多个步骤, 最终形成一个具有更大波长和波高的滚波. 本文发现了在3个滚波间距较近的情况下, 会发生二重聚合现象, 即后两个滚波首先聚合, 然后与前波进一步聚合形成一个新的滚波.      

BOUNDARY CONDITIONS IN SHALLOW WATER MODELS—AN ALTERNATIVE IMPLEMENTATION FOR FINITE ELEMENT CODES

Finite element solution of the shallow water wave equations has found increasing use by researchers and practitioners in the modelling of oceans and coastal areas. Wave equation models, most of which use equal-orderC⁰ interpolants for both the velocity and the surface elevation, do not introduce spurious oscillation modes, hence avoiding the need for artificial or numerical damping. An important question for both primitive equation and wave equation models is the interpretation of boundary conditions. Analysis of the characteristics of the governing equations shows that for most geophysical flows a single condition at each boundary is sufficient, yet there is not a consensus in the literature as to what that boundary condition must be or how it should be implemented in a finite element code. Traditionally (partly because of limited data), surface elevation is specified at open ocean boundaries while the normal flux is specified as zero at land boundaries. In most finite element wave equation models both of these boundary conditions are implemented as essential conditions. Our recent work focuses on alternative ways to numerically implement normal flow boundary conditions with an eye towards improving the mass-conserving properties of wave equation models. A unique finite element formulation using generalized functions demonstrates that boundary conditions should be implemented by treating normal fluxes as natural conditions with the flux interpreted as external to the computational domain. Results from extensive numerical experiments show that the scheme does conserve mass for all parameter values. Furthermore, convergence studies demonstrate that the algorithm is consistent, as residual errors at the boundary diminish as the grid is refined.     

基于VPM-THINC/QQ模型的波浪高保真模拟

为实现波浪传播的高保真数值模拟,采用包含单元均值和点值(volume-average/point-value method,VPM)的有限体积法求解纳维-斯托克斯方程和具有二次曲面性质和高斯积分的双曲正切函数(THINC method with quadratic surface representation and Gaussian quadrature,THINC/QQ)方法来重构自由面,建立以开源求解库OpenFOAM底层函数库为基础的VPM-THINC/QQ模型. 在本模型中添加推板造波法实现波浪的产生功能,采用松弛法实现消波功能,构建高精度黏性流数值波浪水槽. 分别采用VPM-THINC/QQ模型和InterFoam求解器(OpenFOAM软件包中广泛使用的多相流求解器)开展规则波的数值模拟,重点探究网格大小和时间步长等因素对波浪传播过程的影响,定量地分析波高衰减程度;为验证本模型的适应性,对长短波进行模拟. 结果表明,在相同网格大小或时间步长条件下,VPM-THINC/QQ模型的预测结果与参考值吻合较好,波高衰减较少,且无相位差,在波浪传播过程的模拟中呈现出良好的保真性. 本文工作 为波浪传播的模拟研究提供了一种高精度的黏性数值波浪水槽模型.      

非稳态不可压缩自由表面粘性流体的三维数值计算

扩展了相对体积算法，计算了变速旋转的敞口圆筒内水的真实非稳态流动。采用了原始变量、交错非等分网格和显式迭代。计算结果与实验现象相吻合。当圆筒长时间等速旋转，其内流体与筒体一起作刚性旋转时，计算自由表面形状与流体力学理论公式的预言吻合得很好。     

A WAVE EQUATION MODEL TO SOLVE THE MULTIDIMENSIONAL TRANSPORT EQUATION

The wave equation model, originally developed to solve the advection–diffusion equation, is extended to the multidimensional transport equation in which the advection velocities vary in space and time. The size of the advection term with respect to the diffusion term is arbitrary. An operator-splitting method is adopted to solve the transport equation. The advection and diffusion equations are solved separate ly at each time step. During the advection phase the advection equation is solved using the wave equation model. Consistency of the first-order advection equation and the second-order wave equation is established. A finite element method with mass lumping is employed to calculate the three-dimensional advection of both a Gaussian cylinder and sphere in both translational and rotational flow fields. The numerical solutions are accurate in comparison with the exact solutions. The numerical results indicate that (i) the wave equation model introduces minimal numerical oscillation, (ii) mass lumping reduces the computational costs and does not significantly degrade the numerical solutions and (iii) the solution accuracy is relatively independent of the Courant number provided that a stability constraint is satisfied. © 1997 by John Wiley & Sons, Ltd.     

关于自由面压力脉动与摇板造波的等价性

考虑了一个逆问题，即在浮体运动和自由面压力分布之间是否存在某种等价性？作为这一方向努力的一部分，从二维半无限长水槽摇板造波的特例出发考察了这个问题．基于线性势流理论，导出了自由面压力分布应满足的带复数核的第一类Ｆｒｅｄｈｏｌｍ积分方程，并用正则化方法得到了这类不适定的积分方程的近似正则解．结果表明，自由面压力脉动与摇板造波之间的等价性可以通过解相应的逆问题来解决．     

THE BOUNDARY ELEMENT METHOD (BEM) FOR WAVE EQUATION

The formula of BEM suited to solve the problems of wave propagation in boundlessmedium is obtained from numerical treatment of Kirchhoff integral equation.Afer quotingthe coefficients of refraction and reflection of wave at surface or interface,the expression ofBEM which is suitable for the problems of wave propagation in multi-isotropic mediums isalso given.     

An explicit formulation for the evolution of nonlinear surface waves interacting with a submerged body

An explicit formulation to study nonlinear waves interacting with a submerged body in an ideal fluid of infinite depth is presented. The formulation allows one to decompose the nonlinear wave–body interaction problem into body and free‐surface problems. After the decomposition, the body problem satisfies a modified body boundary condition in an unbounded fluid domain, while the free‐surface problem satisfies modified nonlinear free‐surface boundary conditions. It is then shown that the nonlinear free‐surface problem can be further reduced to a closed system of two nonlinear evolution equations expanded in infinite series for the free‐surface elevation and the velocity potential at the free surface. For numerical experiments, the body problem is solved using a distribution of singularities along the body surface and the system of evolution equations, truncated at third order in wave steepness, is then solved using a pseudo‐spectral method based on the fast Fourier transform. A circular cylinder translating steadily near the free surface is considered and it is found that our numerical solutions show excellent agreement with the fully nonlinear solution using a boundary integral method. We further validate our solutions for a submerged circular cylinder oscillating vertically or fixed under incoming nonlinear waves with other analytical and numerical results. Copyright © 2007 John Wiley & Sons, Ltd.     

非均匀水流水域波浪的传播变形

将两个不同的、考虑波流相互作用和能量耗散项的、依赖时间变化的双曲型缓坡方程分别化 为一组等价的控制方程组，具体分析了底摩阻项对相对频率和波数矢的影响，从而选择了合 适的数学模型. 将所选择的缓坡方程化为依赖时间变化的抛物型方程，并用ADI法进 行数值求解，建立了缓变水深水域非均匀水流中波浪传播的数值模拟模型. 通过和波流共线 的解析解的比较，说明数值解和解析解相一致. 结合Arthur(1950)水流这一经典算例，定 量地讨论了考虑联合折射-绕射作用后的波数和仅考虑折射作用的波数的差别及其对波高分 布的影响. 在基本同样的条件下, 本文的数值解与他人的计算结果一致.     

On the accuracy of the desingularized boundary integral method in free surface flow problems

In this paper the numerical properties of the desingularized boundary integral formulation were studied within the framework of free surface potential problems. Several numerical experiments were carried out on simple test cases in order to investigate the effects on the accuracy of the distance between the singularity sheet and the free boundary. The optimum value of this distance was related to the mesh size by simple correlations. Once the desingularized boundary integral formulation had been so calibrated, it was implemented for the solution of two typical free surface flow problems: wave diffraction around a fixed obstacle and wave resistance of submerged bodies. Numerical results are discussed in comparison with experimental data; the computational efficiency and accuracy of desingularized algorithms are confirmed and specified. © 1997 John Wiley & Sons, Ltd.     

各向异性介质中弹性波的数值模拟

提出了一种非均匀各向异性介质中弹性波传播的数值模拟算法。该方法可以灵活地运用于具有任意地表形状、内部孔洞、固液边界和不规则内部交界面的介质情况,另外,该方法自然满足复杂几何边界的自由表面条件。这种基于三角形和四边形离散网格的算法使用的是围绕每个节点的积分平衡方程,而不是其它有限差分法中使用的各个节点满足的弹性动力学的微分方程。该文工作是非均匀各向同性介质中弹性波传播格子法研究的继续。除了研究各向异性介质中波的传播以外,还给出了一种能够省时的四边形网格的格子法。     

考虑场地介质随机特性的无限域波动分析

针对场地介质具有随机特性的无限域地震波动分析问题，在概率空间中将随机反应向量按随机介质场离散所得主导随机变量的正交多项式级数形式展开，使随机微分方程变换确定性的扩阶线性方程组，并在波动的元模拟技术的基础上，构造了扩阶透射人工边界公式，两者结合形成了求解无限域随机介质中波动传播问题的有限元分析方法，该方法不仅不受基于摄动思想各类方法的久期项的干扰，而且避免了采用模拟方法时人工边界区单元参数样本不均匀所引起的数值计算不稳定问题。     

无黏流体与固体界面的漏瑞利波

漏瑞利波存在于半无限无黏性流体和半无限固体媒质的界面处. 首先推导流固无限各向同性介质界面处漏瑞利波的特征方程和位移及应力的解析计算公式. 然后结合典型结构通过数值计算研究了漏瑞利波特性以及位移和应力在流体和固体中的分布规律. 数值计算结果表明漏瑞利波的相速度和衰减随流固密度比的增大而增大, 在流固界面上法向位移连续而切向位移不连续. 流固密度比对固体媒质中沿垂直于漏瑞利波的传播方向的位移、正应力和剪应力有比较大的影响,而对沿漏瑞利波的传播方向的正应力几乎没影响. 为利用漏瑞利波的无损检测与评价提供了理论基础.      

THE SEMI-DISCREIXTE METHOD FOR SOLVING HIGH-DIMENSION WAVE EQUATION

1.IntroductionWaveequationiswidelyusedinsuchsubjectsasgeophysics,elasticmechanics,andsoon.Therefore,how'tosolvewaveequationbecomesaveryimportantproblem.Althoughpeoplehaveachievedalotinthetheoryandcalculationofwaveequationl']'121,newproblemsandsolutionskeep.comingoutl3]'141.Oneofthemethodsgiveninpaper[5]istoreducetwodimensionequationtoone-dimensionequationsystem.However,itisdifficulttoextendhighdimensionwave'equationandwaveequationwithvariablecoefficient.Bythesemi-discrete'methoddiscussedinthi…     

Free surface wave motions and interactions

This paper investigates the problems involved in the numerical simulation of free surface wave motions and surface wave effects on marine structures. Various approaches that might be taken in meeting these problems are discussed, and their relative advantages and disadvantages are considered. One particular approach combines a Lagrangian formulation of the governing equations, a triangular grid and a finite-difference solution procedure. Since this approach has some distinct advantages in the numerical calculation of fluid flows which include a free surface, it formed the basis for the development of one particular computer code, SPLISH. Sufficient progress has been made with the SPLISH code to demonstrate the attractiveness of numerical calculations for wave flow problems. Recent computational results demonstrate that realistic time-varying local flow fields, pressures and forces on and near structures such as a half-cyclinder on the ocean floor can be determined from numerical calculations for certain conditions. Good agreement is found in comparison of the numerical results from SPLISH, recent linear wave Green's function and fifth-order asymptotic solutions for wave motion over a bottom seated half-cylinder, and an experimental simulation in a wave channel.