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.     

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。     

海岸波浪场模型研究进展

从建模原理、波浪在近岸区域传播的众多机制、模型的类别、优势、局限性以及模型在未来的发展趋势等方面,综述了在海岸工程实践中广泛运用的以下两大类海岸波浪场预测模型的最新研究进展:(1)能量平衡模型.它一般用来预测海洋深水波候,已发展到相当完善的阶段,例如,最为著名的WAM3G模型.这种模型在海岸工程中的作用就在于可以模拟施加在波浪上的随时间变化的风场效应.(2)质量、动量守恒模型.它在海岸工程中应用最为普遍,并且内容丰富,数值技巧多样.目前包含了以下代表性的模型:缓坡方程、抛物型方程、非线性浅水方程、高阶Boussinesq型方程、Green-Naghdi理论.      

破碎带波浪的数值模拟

基于一组色散关系得到改进的完全非线性Boussinesq方程建立了一个波浪模型可以模拟近岸水域的波浪变浅、破碎以及在海滩上的爬高等多种变形。波浪破碎引起的能量衰减是在动量方程中引入一个在空间和时间上都只作用于波前的涡粘项来模拟。动海岸线边界用窄缝法处理。波浪爬高用非线性浅水方程推导的非破碎波浪在斜坡上爬高的解析解来验证。本模型还模拟了波浪在斜坡上不同类型的破碎变形过程,并将其波高和平均水位的沿程变化和物理模型实验的结果比较,两者符合良好。     

黄茅海波-流共同作用下的三维悬沙数值模拟

针对黄茅海河口区波流相互作用显著、三维空间结构明显及泥沙运动复杂等特点,联合第3代海浪模式SWAN,建立了波流共同作用下的三维悬沙数学模型.在水流计算中,考虑了波浪产生的辐射应力影响,波浪依赖的表面风应力影响及波浪影响下的底部剪切应力,并采用k-kl紊流闭合模型提供垂向涡粘系数和垂向扩散系数.悬沙扩散方程中的源函数利用切应力法确定,泥沙沉降速度考虑絮凝作用,从而提高黄茅海悬沙场数值模拟精度.通过含沙量实测资料验证,模拟值与实测值符合较好.在模型验证的基础上,讨论了不考虑波浪与考虑波浪两种情况下黄茅海的悬沙分布特征,为工程实际研究提供了依据.     

波浪破碎的一种混合湍流模拟模式

近岸波浪的变形与破碎,一方面影响水体标识码运输,另一方面对消波护岸具有指导意义.本文提出一种三维混合湍流模拟模式方法,将求解区域分为造波区、波浪传播区和消波区. 造波区采用层流模式,通过基于 Fluent 的二次开发的 UDF 方法在边界进行速度造波.这种方法在给定入口速度的条件标识码据已知波高进行 精准插值,从而控制水的体积分数. 在波浪传播区域,采用大涡标识码行模拟研究,在消波区,采用 RANS 模型并利用多孔介质消波法进行消波. 模标识码 VOF 方法捕捉波浪破碎过程中的自由面变化.本文对波高为 5.5cm 的规则波 (M1)、波高为 13.5cm 的 规则波 (M3)、有效标识码 7.75cm 的 TMA 谱单向不规则波 (U1) 和有效波高为 19cm 的 TMA 谱多向不规则波 (B5) 展开标识码研究,并与前人的相关标识码果作比较,各条件下模拟结果与实验结果吻合.模拟结果说明本文提出的模型能够准确模拟出波浪传播过程中的折射和标识码象,并且能够捕捉的波浪破碎过程中的自由面变化,为三维波浪的传播与破碎的数值模拟提供一种模拟方法.      

海岸碎波拍的计算

研究了一维碎波拍的计算方法．波浪控制方程由欧拉方程在短波周期上平均而得到．为了考虑低频波浪在海岸上的破碎，采用了ＷＡＦ（ＷｅｉｇｈｔｅｄＡｖｅｒａｇｅＦｌｕｘ）方法求解长波方程．对由辐射应力和海底摩擦力引起的方程非齐次项采用了时间算子分裂法进行了处理，并对由此产生的误差进行了修正．计算了单色波和双色波垂直入射海岸的情况，并与实验结果进行了对比．     

非均匀水流中非线性波传播的数值模拟

以一种考虑波流相互作用的新型{Boussinesq}型方程为控制方程组， 采用五阶{Runge}-{Kutta}-{England}格式离散时间积分，采用七点 差分格式离散空间导数，并通过采用恰当的出流边界条件，从而建立了非均匀水流中非线性 波传播的数值模拟模型. 通过对均匀水流与水深水域内和潜堤地形上存在弱流或强流时波浪 传播的数值模拟，说明模型能有效地反映水流对波浪传播的影响.     

海堤越浪的数值模拟

基于RANS方程和两方程湍流模型,采用有限体积法,将人射波波场作为人工的分布源项加人动量方程,提出了适用于VOF方法的源造波一消波技术。通过对行波及驻波的计算,分别考察了数值波浪水槽前端及末端消波段的有效性。在本文建立的数值波浪水槽内对规则波在海堤上爬高和越浪过程进行了数值模拟,并将计算结果与现有实验结果进行了比较。验证计算结果表明,数值模拟结果较好地复演了海堤越浪过程。为了研究模型尺度对越浪量的影响,文中设计了一组满足重力相似但具有不同几何比尺的数值实验模型。系列数值实验结果表明,若按重力相似换算越浪量,计算结果与实验预报值间的偏差随模型比尺的增大和堤前波浪破碎强度的增强而增大,建议在进行越浪物理模型实验时需进一步考虑模型比尺对原型预报值的影响。     

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。     

Numerical simulation of pollutant transport acted by wave for a shallow water sea bay

A numerical model of pollutant transport acted by water waves on a shallow‐water mild‐slope beach is established in this study. The numerical model is combined with a wave propagation model, a multiple wave‐breaking model, a wave‐induced current model and a pollutant convection–dispersion model. The wave propagation model is based on the higher‐order approximation of parabolic mild‐slope equation which can be used to simulate the wave refraction, diffraction and breaking in a large area of near‐shore zone combined with the wave‐breaking model. The wave‐induced current model is established using the concept of the radiation stress and considering the effect of bottom resistance caused by waves. The numerical model is verified by laboratory experiment results of regular and irregular waves over two mild beaches with different slopes. The numerical results agree well with experimental results. The numerical model has been applied in the near‐shore zone of Bohai bay in China. It is concluded that pollutant transport parallel to the shoreline due to the action of waves, which will induce serious pollution on the beach. Copyright © 2005 John Wiley & Sons, Ltd.     

A new numerical model for simulations of wave transformation,breaking and long‐shore currents in complex coastal regions

In this paper, we propose a model based on a new contravariant integral form of the fully nonlinear Boussinesq equations in order to simulate wave transformation phenomena, wave breaking, and nearshore currents in computational domains representing the complex morphology of real coastal regions. The aforementioned contravariant integral form, in which Christoffel symbols are absent, is characterized by the fact that the continuity equation does not include any dispersive term. A procedure developed in order to correct errors related to the difficulties of numerically satisfying the metric identities in the numerical integration of fully nonlinear Boussinesq equation on generalized boundary‐conforming grids is presented. The Boussinesq equation system is numerically solved by a hybrid finite volume–finite difference scheme. The proposed high‐order upwind weighted essentially non‐oscillatory finite volume scheme involves an exact Riemann solver and is based on a genuinely two‐dimensional reconstruction procedure, which uses a convex combination of biquadratic polynomials. The wave breaking is represented by discontinuities of the weak solution of the integral form of the nonlinear shallow water equations. The capacity of the proposed model to correctly represent wave propagation, wave breaking, and wave‐induced currents is verified against test cases present in the literature. The results obtained are compared with experimental measures, analytical solutions, or alternative numerical solutions. Copyright © 2015 John Wiley & Sons, Ltd.     

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．      

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.     

Improvement of moving particle semi‐implicit method for simulation of progressive water waves

Precise simulation of the propagation of surface water waves, especially when involving breaking wave, takes a significant place in computational fluid dynamics. Because of the strong nonlinear properties, the treatment of large surface deformation of free surface flow has always been a challenging work in the development of numerical models. In this paper, the moving particle semi‐implicit (MPS) method, an entirely Lagrangian method, is modified to simulate wave motion in a 2‐D numerical wave flume preferably. In terms of consecutive pressure distribution, a new and simple free surface detection criterion is proposed to enhance the free surface recognition in the MPS method. In addition, a revised gradient model is deduced to diminish the effect of nonuniform particle distribution and then to reduce the numerical wave attenuation occurring in the original MPS model. The applicability and stability of the improved MPS method are firstly demonstrated by the calculation of hydrostatic problem. It is revealed that these modifications are effective to suppress the pressure oscillation, weaken the local particle clustering, and boost the stability of numerical algorithm. It is then applied to investigate the propagation of progressive waves on a flat bed and the wave breaking on a mild slope. Comparisons with the analytical solutions and experimental results indicate that the improved MPS model can give better results about the profiles and heights of surface waves in contrast with the previous MPS models. Copyright © 2017 John Wiley & Sons, Ltd.     

Experimental study and numerical simulation of mean longshore current for mild slope

In this paper, experimental and numerical studies were performed to investigate the characteristics of longshore current under two mild slopes, the results of which may complement the existing studies, which have mainly focused on steep slopes. The experimental results revealed that the average velocity distribution of the longshore current was significantly different under the two different mild slopes. Under the slope of 1:100, the distribution of the averaged longshore current velocity had a downward concave trend at the nearshore side, while under the slope of 1:40 the trend became convex. In addition, the analysis of the numerical results showed that the distribution of the averaged longshore current velocity was affected by the distribution of the wave height within the surf zone and the bottom friction equations, with the influence of the latter being more significant. For the slope of 1:100, the cross-shore variability of alongshore variability can be calculated using the flow-type bottom friction equation, while for the slope of 1:40, the wave-type bottom friction equation can be used instead. Finally, the secondary breaking wave heights for mild slopes and the distribution of wave set-up are also shown in the study.     

流动系统中爆轰波传播特性的数值模拟

基于带化学反应的二维Euler方程,采用氢气/空气的9组分19步基元反应简化模型,对充有当量 比的氢气/空气预混气体的矩形爆轰流场中爆轰波的传播过程进行了数值模拟,讨论了均匀来流对爆轰波传 播的影响。数值结果表明,在均匀来流的影响下,上游方向上的燃烧强度大于C-J爆速,下游方向上的燃烧强 度小于C-J爆速;上游方向传播的爆轰波的阵面压力大于下游方向传播的爆轰波的阵面压力。所以,经典的 C-J爆轰理论并不适用于流动系统中爆轰波传播特性的研究。