三维缓变流场上波浪折射—绕射的缓坡方程

运用Luke变分原理,建立了波浪在三维缓变流场中和缓变海底上折射-绕射的一般缓坡方程,据此给出了在几何-光学逼近（△↓S)^2=k^2有效时,波浪、环境流和海底坡度必须满足的若干条件,对一般缓坡方程进行了分类,在一种特定流场结构的假定下,得到了方程的行波解。     

非结构化网格下大范围波浪的折绕射计算

从含流缓坡方程出发,推导出光程函数方程。采用基于非结构化网格下的有限体积法对光程函数方程和波作用守恒方程进行数值离散和联合求解,从而构建了一个考虑绕射的计算近岸大范围波浪传播过程的数值模型。模型的空间步长不再受制于波长的限制,同时非结构化网格可以很好地拟合复杂岸线变形。模型分别通过了施奈尔定律、直立防波堤后的波浪绕射和圆形浅滩上的波浪变形验证,结果表明,该数值模式能有效模拟复杂边界条件和大范围水域下近岸波浪的传播过程中的折射和绕射等变形。     

轴对称管口激波绕射诱导的复杂两相流动的数值分析

基于稀颗粒群假定下的双流体简化模型,采用具有高精度、高分辨率的数值方法,研究了粉尘气体中轴对称管口激波绕射诱导的复杂两相流动。得到非平衡两相流动不同于纯气体流动的一些基本物理特征,以及粒子物性参数改变对这些特性的影响。     

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.     

二维溃坝波的反射与绕射

本文推导了间断分解公式,建立了Godunov型格式,研究了二维溃坝波的传播、反射和绕射。计算结果符合物理实际,令人满意。方法是有效的,可以提供水工部门作为设计和防护的依据。     

应力波在缺口处绕射传播的实验研究

本文采用动光弹技术对应力波遭遇到缺口边界时的绕射传播现象进行了初步实验研究,并对所产生的应力集中及动态断裂进行了半定量分析,本文研究可供目前广泛采用的控制爆破法拆除旧建筑物和废设备基础的工作提供参考。     

波浪与外壁开孔双筒柱群的相互作用

应用速度势的特征函数展开和透空壁内两壁间压力差和流体速度成正比的线性模型,建立 了波浪与外壁开孔同轴双筒桩柱群相互作用的线性解析解. 应用这一模型进行了数值计算, 用以检验孔隙系数对双筒柱上的波浪力和波面高度的影响. 结果表明,外壁孔隙系数的增加 对减小波浪力和柱外波面高度有很大影响.     

随机波浪作用下近岸波流场的数值模拟

结合近岸波浪抛物型缓坡模型和近岸波流场模型,对近岸不规则波浪及其破碎后所产生的流场进行了数值模拟. 在不规则波浪场的模拟中,采用JONSWAP波浪谱对入射单向不规则波浪要素按等分频率法进行离散,应用考虑波浪不规则性和破碎效应的抛物型缓坡方程对波浪场进行数值模拟,并基于抛物型缓坡方程中的波浪势函数等参数计算波浪辐射应力,以波浪辐射应力为主要动力因素基于近岸流数学模型对近岸波浪破碎所产生的近岸流场进行数值模拟,并对数值模拟结果进行了验证. 模拟结果表明该模型可有效地用于研究波浪破碎产生的近岸波流场.      

环形激波绕射、反射和聚焦流场的间断有限元模拟

采用间断有限元方法对环形激波在圆柱形激波管内绕射、反射和聚焦流场进行了数值模拟。将二维守恒方程的间断有限元方法发展到轴对称Euler方程,并对环形激波绕后台阶流动进行了数值计算。计算结果表明,采用间断有限元方法能够有效地捕捉运动激波在圆柱形激波管内传播的复杂流场结构;在聚焦点附近,数值解具有较大的梯度变化,表明该方法对间断解具有较强的捕捉能力,在聚焦点附近不会产生振荡或抹平间断现象。     

基于ABAQUS的小尺度桩柱波浪力计算方法

基于达索公司开发的ABAQUS有限元分析软件,利用ABAQUS提供的用户子程序编制程序,计算分析风电机组在海洋环境中受到的波浪力.在计算中,使用了三维梁单元和壳单元建模,应用线性波模拟海洋环境中的波浪.基于莫里森方程和数值积分的方法,分析桩柱形支撑结构上的波浪载荷,计算支撑结构的位移,应力变化等,得到了较好的结果.     

NUMERICAL SIMULATION OF SHALLOW WATER WAVE PROPAGATION USING A BOUNDARY ELEMENT WAVE EQUATION MODEL

The present paper makes use of a wave equation formulation of the primitive shallow water equations to simulate one-dimensional free surface flow. A numerical formulation of the boundary element method is then developed to solve the wave continuity equation using a time-dependent fundamental solution, while an explicit finite difference scheme is used to derive velocities from the primitive momentum equation. One-dimensional free surface flows in open channels are treated and the results compared with analytical and numerical solutions. © 1997 John Wiley & Sons, Ltd.     

浅水孤立波在三维浮体上的绕射

浅水域中非线性水波运动的控制方程通常是经过深度平均的Boussinesq方程。然而,这一方程在浮体近旁或水下障碍物附近不再适用,在这些区域,流动在水深方向的变化不容忽略,本文应用匹配渐近展开法和边缘层(edge layer)思想,建立了浅水弱非线性波与三维浮体相互作用的数学模型,作为算例,求解了浅水孤立波在垂直圆柱形浮体上的绕射.本方法可以推广到波在一般浮体上绕射的情况。     

论弹性波绕射与动应力集中问题

本文综述了弹性波绕射与动应力集中问题的复变函数解法,给出了单连通问题、多连通问题及多裂纹问题的具体求解过程及算式.      

MODELLING OF WAVE PROPAGATION IN THE NEARSHORE REGION USING THE MILD SLOPE EQUATION WITH GMRES-BASED ITERATIVE SOLVERS

The mild slope equation in its linear and non-linear forms is used for the modelling of nearshore wave propagation. The finite difference method is used to descretize the governing elliptic equations and the resulting system of equations is solved using GMRES-based iterative method. The original GMRES solution technique of Saad and Schultz is not directly applicable to the present case owing to the complex coefficient matrix. The simpler GMRES algorithm of Walker and Zhou is used as the core solver, making the upper Hessenberg factorization unneccessary when solving the least squares problem. Several preconditioning-based acceleration strategies are tested and the results show that the GMRES-based iteration scheme performs very well and leads to monotonic convergence for all the test-cases considered.     

A compact numerical algorithm for solving the time‐dependent mild slope equation

The mild slope equation has been widely used to describe combined wave refraction and diffraction. In this study, a new numerical algorithm is developed to solve the time‐dependent mild slope equation in a second‐order hyperbolic form. The numerical algorithm is based on a compact and explicit finite difference method that is second‐order accurate in both time and space. The algorithm has the similar structure to the leap‐frog method but is constructed on three time levels for the second‐order time derivative term. The numerical model has the capability of simulating transient wave motion by correctly predicting the speed of wave energy propagation, which is important for the real‐time forecast of the arrival time of storm waves generated in the far field. The model is validated against analytical solution for wave shoaling and experimental data for combined wave refraction and diffraction over a submerged elliptic shoal on a slope (Coastal Eng. 1982; 6 :255). Lastly, the realistic scale Homma's island (Geophys. Mag. 1950; 21 :199) is studied with the use of various wave periods of T = 720s, T = 120 s, and T = 24 s. These wave periods correspond to long, intermediate, and short waves for the given topography, respectively. Comparisons are made between numerical results and existing analytical solutions in terms of the wave amplification around the island, which serves as the indicator for the potential wave runup. Excellent agreements are obtained. The model runs on a PC (Pentium IV 1.8GHz) and the computer capacity allows the computation of a mesh system up to 3000 × 3000, which is equivalent to about 150 × 150 waves or a large area of 540km × 540km for a wave train with the period of T = 60 s. Copyright 2004 John Wiley & Sons, Ltd.     

SIMULATION OF WAVE MOTION USING A LATTICE GAS MODEL

The lattice gas model for simulating two-phase flow, proposed by Appert and Zaleski, has been modified by the introduction of gravitational interactions and the new model has been used to simulate standing wave patterns on the free surface of a fluid. The results compare well with linear theory.     

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.