任意水深变化水域非线性波数值模拟

为了较为准确地计算沙质海岸沿岸输沙率,基于网格模型建立沙质海岸波浪的传播变化模型,根据求得的波高和波向分布特征,并考虑辐射应力等,计算波生流的分布。并在此基础上通过波浪最大底部轨道速度和沿岸流的分布特点,建立估算破波带内各网格单元上沿岸输沙率的分布模型。     

任意水深变化Boussinesq型方程非线性波数值计算

首先从一个含有耗散项的高阶非线性和频散性波浪理论模型出发,建立了适用于任意底坡变化,相对水深h／Lo≤1的非线性波数学模型。应用全隐式交错网格和二阶精度中心差分法。得到离散方程组。进一步对其一阶导数项进行修正,达到与方程高阶项同量阶精度。精度检验表明本文计算结果与理论解和物理模型结果符合良好。     

无限水深聚焦波完全非线性数值模拟

基于势流理论提出一种新的高阶边界元方法对无限水深的聚焦波浪进行完全非线性数值模拟.自由水面满足完全非线性边界条件,模拟波浪的非线性效果可以达到更高阶.利用镜像原理,建立一种全新的格林函数应用到无限水深的数值波浪水槽中,以致于两无限深水槽侧壁的积分可以被排除.为了产生相应的入射波和吸收出流波浪,一个由点源组成的造波装置被布置于计算域内,同时人工阻尼层被用来吸引出流波浪,由波浪聚焦的方法得到极限波浪.通过开展线性和完全非线性聚焦波浪的数值实验及与理论解对比,验证本数值模型可以用来模拟无限深水域的极限波浪,且在出流边界没有反射.     

任意曲线边界条件下缓变水深水域波浪传播的数值模拟

缓坡方程被广泛地应用于描述波浪的传播变形计算,目前一般采用矩形网格求解.将计算域剖分为任意四边形网格,以格林公式为基础,在变量沿单元边界线性变化的假定下,对双曲型的波能守恒方程、波数矢无旋性方程进行离散,同时通过等参单元变换推求节点偏导数值以离散椭圆型光程函数方程,从而建立了任意曲线边界条件下缓变水深水域波浪传播的数值模拟模型.将模型应用于平行直线型等深线地形,并将计算域剖分为不规则四边形网格,对不同入射角、底坡、波高等多种组合情况比较了数值解与解析解,结果表明两者一致.应用于复杂边界的实例,数值模拟结果与物模实验值基本吻合.     

非线性随机波的数值模拟

本文根据作者提出的非线性不规则波四阶近似理论解,首先导出二阶非线性谱和线性谱的关系式,并应用非线性有约束最优化方法建立了从靶谱分解线性谱和二阶非线性谱的数学模式,进而建立非线性随机波数值模拟的数学模型及其快速傅里叶交换算式,从而大大地缩短计算机时。由于采用从靶谱分解出的线性谱,模拟的非线性随机波现实谱和靶谱符合一致。最后通过算例,对模拟的非线性及线性随机波的谱估计及波面统计特性进行初步分析,本方法为浅水不规则波与水流及建筑物相互作用的研究提供随机模拟基础。     

完全非线性深水波的数值模拟

基于势流理论,并结合深水波质点运动从水面向下呈e指数衰减的特性,建立了完全非线性数值变深水槽模型,通过实时模拟活塞式造波机运动来产生波浪.采用时域高阶边界元法进行模拟,利用混合欧拉-拉格朗日方法和四阶Runge-Kutta方法追踪流体瞬时水面,应用镜像格林函数消除了水槽两个侧面的积分,在水槽末端布置人工阻尼层来消除反射...     

二维非线性浅水波的数值模拟

研究工作的目的在于建立一个能够模拟二维潮流、洪水波(长波)和浅水波浪(短波)的综合数学模型.基本模型建立在非线性的Boussinesq方程基础之上.本文主要讨论浅水波浪即短波的数值模拟.模型可以考虑必要的外力项,如柯氏力、风应力、大气压力和底摩阻力等.针对Boussinesq方程提出了一个全隐的二维差分格式,讨论了人工开边界的处理方法.模型被用来计算了突然扩张渠槽中的环流和单突堤后的水波绕射,取得了满意的结果.     

有限水深海流感应电磁场数值模拟

海水是一种高电导率的流体。不停运动的海水因切割地磁场而产生感应电流,从而产生感应电磁场。本文从麦克斯韦方程出发推导了地磁场三分量作用下一维海流感应磁场表达式,并分析了地磁场水平分量对海流感应电磁场的影响。计算表明地磁场水平分量的影响随纬度变化。在高纬度地区地磁场水平分量对海流感应电磁场影响很小,而在低纬度地区它会对海流感应电磁场产生明显的影响。本文还分析了变化的海水电导率对海流感应电磁场的影响。     

渤海岸线及水深变化对水动力影响的数值模拟

为探究渤海岸线及水深变化对水动力的影响,基于Delft3D水动力学模型,选用2003年和2015年作为围 填海前后的典型年份,建立了围填海前后岸线及水深条件下的渤海三维水动力模型,并对水动力场进行了模拟。通过对围填海前后潮波和潮余流的分析,得到了岸线及水深变化对渤海水动力场的影响。结果表明:填海后,岸线及水深变化会对渤海主导分潮M₂分潮产生较大影响,秦皇岛附近无潮点向西北方向偏移,渤海海域M₂ 分潮振幅总体减小;潮致余流场受岸线及水深变化影响较大,其中渤海湾曹妃甸港南部形成复杂的涡流,沿岸海域余流增大;滨海新区附近形成多个小范围环流,且天津港到黄骅港北部沿岸海域2015年余流比2003年增加3~5 cm/s;黄骅港南部形成一个逆时针环流,并且该处余流减小2~5 cm/s。辽东湾辽河口附近由于水深增加导致余流减小2~7 cm/s。莱州湾黄河口附近的逆时针环流向东南方向移动,黄河口北部余流略有减小,东南部余流明显增大,增加量最多能达到9 cm/s。刁龙嘴南侧顺时针环流减小,北侧顺时针环流增大4~9 cm/s。     

非线性波传播的新型数值模拟模型及其实验验证

以一种新型的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,从而建立了非线性波传播的新型数值模拟模型.通过对均匀水深水域内波浪传播的数值模拟说明,模型能较好地模拟大水深水域和强非线性波的传播.通过设置不同的入射波参数来进行潜堤地形上波浪传播的物理模型实验,并将数值解与物理模型实验结果进行了比较.     

Numerical Simulation of Nonlinear Three Dimensional Waves in Water of Arbitrary Varying Topography

—The numerical simulation is based on the authors＇high-order models with a dissipative termfor nonlinear and dispersive wave in water of varying depth.Corresponding finite-difference equations andgeneral conditions for open and fixed natural boundaries with an arbitrary reflection coefficient and phaseshift are also given in this paper.The systematical tests of numerical simulation show that the theoreticalmodels,the finite-difference algorithms and the boundary conditions can give good calculation results forthe wave propagating in shallow and deep water with an arbitrary slope varying from gentle to steep.     

High-Order Models of Nonlinear and Dispersive Wave in Water of Varying Depth with Arbitrary Sloping Bottom

High-order models with a dissipative term for nonlinear and dispersive wave in water of va-rying depth with an arbitrary sloping bottom are presented in this article.First,the formal derivations toany high order of μ(=h/λ,depth to deep-water wave length ratio)and ε(=α/h,wave amplitude todepth ratio)for velocity potential,particle velocity vector,pressure and the Boussinesq-type equations forsurface elevation η and horizontal velocity vector U at any given level in water are given.Then,the exactexplicit expressions to the fourth order of μ are derived.Finally,the linear solutions of η,U,C(phase ce-lerity)and C_g(group velocity)for a constant water depth are obtained.Compared with the Airy theory,excellent results can be found even for a water depth as large as the wave legnth.The present high-ordermodels are applicable to nonlinear regular and irregular waves in water of any varying depth(from shal-low to deep)and bottom slope(from mild to steep).     

Numerical Modeling of Wave Diffraction-Refraction in Water of Varying Current and Topography

—A numerical model for wave diffraction-refraction in water of varying current and topogra-phy is proposed,and time-dependent wave mild-slope equation with a dissipation term and correspondingequivalent governing equations are presented.Two different expressions of parabolic approximations forthe case of the absence of current are also given and analyzed.The influence of current on the results ofsimulation of waves is discussed.Some examples show that the present model is better than others in simu-lating wave transformation in large water areas.And they also show that the influence of current shouldbe taken into account,on numerical modeling of wave propagation in water of strong current and coastalareas,otherwise the modeling results will be largely distorted.     

Numerical Analysis of Wave Forces on Arbitrarily Shaped Multi-Pillars Over Varying Topography

The modified hybrid element method (MHEM) is utilized to predict and analyze wave forces on arbitrarily shaped multiple bodies. This method can be applied to waves of all water depths, i. e. shallow, intermediate, and deep waters, on slowly varying seabed. The MHEM employs the ICCG method to save CPU and storage, thus the computation of wave forces for large multi-body systems can be carried out on microcomputers. Numerical results of the present method are compared with experimental data and other solutions. It is shown that the MHEM provides more accurate solutions of the wave forces than other numerical methods do. Therefore, the methodology presented herein can be used in the design of coastal and ocean structures.     

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 in waterof slowly varying current and topography is developed in this paper.And corresponding theoretical modelincluding the dissipation term is briefly described,together with some analysis and comparison ofcomputational 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 engineeringpractice.     

Numerical Simulation of Non-Linear Wave Propagation in Waters of Mildly Varying Topography with Complicated Boundary

In this paper, the characteristics of different forms of mild slope equations for non-linear wave are analyzed, and new non-linear theoretic models for wave propagation are presented, with non-linear terms added to the mild slope equations for non-stationary linear waves and dissipative effects considered. Numerical simulation models are developed of non-linear wave propagation for waters of mildly varying topography with complicated boundary, and the effects are studied of different non-linear corrections on calculation results of extended mild slope equations. Systematical numerical simulation tests show that the present models can effectively reflect non-linear effects.     

Water Wave Refraction and Diffraction over Frictional Topography

- This paper considers the effects of wave energy dissipation induced by sea-bottom friction on the computational results of water wave refraction and diffraction with the parabolic equation method. The presented results show that the friction factor formula adopted in this paper is of higher numerical accuracy than that introduced by Dalrymphe (1984), and it can be used to compute wave propagation over large open areas.     

复杂地形下海浪数值模式的特征线计算格式

LAGFD-WAM海浪数值模式是一种第三代海浪数值模式，通过求解波数谱平衡方程，并考虑风输入、波浪破碎耗散、底摩擦耗散、波波非线性相互作用和波流相互作用等源函数，模拟波数空间下的海浪方向谱，并依此获得海浪的波高、周期和平均波向。该模式的一个显著特点是采用特征线嵌入格式求解海浪的传播。在进行浅水区域的海浪模拟时，特征线嵌入格式的数值计算方案是否合理对海浪数值模拟结果产生直接的影响。为此LAGFD-WAM海浪数值模式提出了一种新的特征线混合数值计算格式，并应用于浅水海浪数值模拟。结果表明，采用该计算方法，能够使数值模拟结果与实测结果很好符合。     

Nonlinear Effect of Wave Propagation in Shallow Water

—In this paper,a nonlinear model is presented to describe wave transformation in shallow wat-er with the zero-vorticity equation of wave-number vector and energy conservation equation.Thenonlinear effect due to an empirical dispersion relation(by Hedges)is compared with that of Dalrymple＇sdispersion relation.The model is tested against the laboratory measurements for the case of a submergedelliptical shoal on a slope beach,where both refraction and diffraction are significant.The computation re-sults,compared with those obtained through linear dispersion relation.show that the nonlinear effect ofwave transformation in shallow water is important.And the empirical dispersion relation is suitable for re-searching the nonlinearity of wave in shallow water.