高阶Boussinesq水波方程数值模型及其与实验结果的对比

本文建立了基于预报-校正差分格式的高阶Boussinesq方程数值模型，进行了有沙坝地形上非线性波浪传播的物理模型实验，检验了数值模型和高阶Boussinesq方程的精度。研究了非线性波浪在有沙坝地形上传播的特性，分析沙坝坡度和水深的影响。     

基于Boussinesq方程的近岸波流统一模型

用统一的理论正确描述近岸海域内不同尺度的水动力学现象是海岸水动力学研究的一个难题.本文通过将一种简单的波浪破碎模型引入到Boussinesq方程,建立了能够统一描述近岸水波和波生流的数学模型.将数学模型应用于计算浅滩上的波浪变形以及均一斜坡上平行于海岸的沙坝缺口附近的波生流,得到了良好的结果.     

近岸波浪及沿岸流数值模拟研究

利用抛物型缓坡方程计算波浪场,并以波浪辐射应力为近岸动力因素,建立深度平均的二维近岸流的控制方程。运用该近岸流方程,对美国Santa Barbara Leadbetter海岸波浪斜向入射所产生的波浪场及波浪破碎所形成的沿岸流进了数值模拟,其中抛物型缓坡模型采用Crank-Nicolson格式进行数值离散,近岸流方程采用ADI差分格式离散。与现场实测资料的对比表明,无论考虑或不考虑波浪非线性因子,模拟结果与实测结果均吻合良好。     

海岸裂流的浮子示踪法实验测量

研究模型实验中采用浮子示踪法测量沙坝海岸裂流的方法,讨论了该方法的具体技术实现和测量结果的精度。实验中裂流由波浪在垂直岸线的直墙上的反射所形成的两列交叉的波浪生成。通过处理CCD图像的浮子轨迹得到了流场的详细速度分布,如旋涡分布等,显示了该方法优于流速仪定点测量的一些特点。与ADV流速仪测量结果的对比表明,由浮子轨迹得到的表层平均流速具有可靠的精度,特别是也可以应用于波浪破碎产生的裂流这样复杂流场的测量。     

基于有限体积法的三维波生近岸流数值模型

波浪破碎产生近岸流是近岸浅水区域一个重要的水动力现象。该文利用辐射应力的概念,并考虑辐射应力沿水深的变化、波浪破碎引起的水滚以及波流共同作用下的水底剪应力,建立了基于有限体积法的三维波生近岸流数值模型。运用建立的数值模型模拟了两个实验室实验,并同实验的实测结果进行了对比。结果表明,建立的数值模型能够较好地模拟波浪破碎产生的近岸流。     

近岸波浪的Boussinesq型方程模拟及其应用

该文首先对近岸波浪数学模型的研究、发展、应用进行了回顾和总结,对各类波浪数学模型的特点进行了简单分析。基于改进的Boussinesq型方程建立了一个完整的近岸波浪数学模型,通过对方程的拓展,综合考虑了模型的造波、消波、动边界处理、波浪破碎等问题。拓展后的数学模型用P-C（预测-校正）法进行数值求解,计算效率高、稳定性好。采用两个经典地形试验数据对模型进行了的验证,数值结果和实验值吻合较好。最后,利用该模型进行了某渔港港池内波浪条件的数值模拟,给出了不同时刻港池内的波面情况,得到了合理的结果。     

风对二维极值波作用的数值研究

实际海域中风浪往往共存,当极值波浪出现时,风会对其特性产生很大影响。为了研究风对极值波浪特性的影响规律,该文基于势流理论建立自由水面满足完全非线性边界条件的风浪混合作用数值水槽模型,通过实时模拟造波板运动产生入射波,并基于波群聚焦原理定点产生极值波浪,利用改进的杰弗里斯遮蔽原理(Jeffreys'sheltering mechanism)将风压引入到自由水面动力边界条件中。在时域模拟中,采用混合欧拉-拉格朗日方法追踪瞬时水面,利用格林第二定理建立了边界积分方程,采用高阶边界元方法进行离散求解。通过与已发表实验结果对比验证模型的准确性,进而开展数值实验研究风对极值波浪水动力特性的影响,包括聚焦幅值、聚焦位置和极值波高随风速的变化以及波群聚焦和解焦过程波浪演变特性等。     

新型高阶Boussinesq水波方程

从经典的Boussinesq方程出发，引入两个参数并对方程中的部分项进行替换，通过严格的数学推导给出量级为O(εμ2)的高阶非线性项，得到一种新型的高阶Boussinesq方程。该方程的色散关系比经典Boussinesq方程提高了一阶，变浅作用性能也得到了改善，方程的适用范围由浅水达到中等水深。利用Crank-Nicloson格式的有限差分法对方程进行数值模型在一维方向上进行离散计算，建立了高阶Boussinesq方程的数值模型。为验证数值模型的正确性，将数值计算结果与Zou等(2001)的物模试验结果以及Beji与Nadaoka方程的数值结果进行对比，本文的数值结果与试验结果吻合程度较好，表明本文方程可适于模拟变水深下的波浪场数值模拟。     

海岸底床剖面演变模拟与分析

近岸水下沙坝的位置与高度是河口海岸底床变化的主要原因,波浪与地形之间的耦合与反馈造成了沙坝向海连续迁移。使用LITPACK的添加模块LITPROF模拟沙质海岸剖面形态变化主要是沙坝的形成与迁移,通过模拟不同波浪入射角及剖面坡度对沙坝形成与迁移的影响,得出沙坝主要在波浪破碎点处形成,波浪入射角增大,沙坝离岸迁移越快;底床坡度越陡,沙坝产生与迁移越快,岸滩变形也越大。     

单沟槽沙坝海岸的裂流实验研究

该文实验研究了单沟槽沙坝海岸上产生的波生裂流流场,重点关注了不同波浪条件下流场水平形态以及最大裂流流速的变化.实验在波浪水槽中进行,采用规则波作为入射波浪,应用高精度浪高仪阵列和流速仪阵列,在全场范围内较密集地采集波面升高和流速数据,通过分析实验数据,获得全场波高、平均水面以及流速分布,对裂流及两个存在的补偿流进行了描述,分别比较和分析了不同波高对于裂流强度及整个流场形态的影响,并对最大离岸流速与波高间的关系进行了分析.     

Simulation of shallow water waves using VOF method

In this study, the transformation of groupy waves and plunging breakers as they travel to a breaking point in a coastal zone is two dimensionally investigated. The governing equations are momentum, continuity and Fractional Volume Of Fluid (VOF) function equations. The fluid is assumed to be viscous and incompressible. Turbulence has been considered using the two equations k-? model. A Simple Line Interface Calculation (SLIC) type VOF method is implemented for calculating VOF flux. The Pressure Implicit with Splitting of Operators (PISO) algorithm in the staggered finite volume method is employed. For the validation of the different aspects of the model, numerical tests are performed to simulate plunging breakers. These tests have shown that the present model is a powerful, reliable tool for simulating water free surface in wave motion and the breaking process. Finally, the model is used for simulating the groupy wave propagation and its breaking. The results have shown that the present model is capable of simulating plunging breakers accurately, and it is also able to track the existence of groupy wave induced long wave. Furthermore, the results show that these long period disturbances can travel towards the shore line even after the breaking of the primary wave system.     

汛期分洪溃坝波的数值模拟

本文以二维长波方程为基础,将文献[1]中介绍的方法应用于模拟溃坝波运动。假设在波还没到达的区域有一层很薄的水层,此水层的存在不影响波的运动;在分洪口门处利用堰流公式,将二维长波方程与一维圣维南方程联立求解,成功地进行了天津市永定河的泄洪能力及汛期分洪的数值预报。     

Numerical simulation of wave transformation,breaking and runup by a contravariant fully non-linear Boussinesq equations model

In this paper we propose a new model based on a contravariant integral form of the fully non-linear Boussinesq equations(FNBE) in order to simulate wave transformation phenomena, wave breaking, runup and nearshore currents in computational domains representing the complex morphology of real coastal regions. The above-mentioned contravariant integral form, in which Christoffel symbols are absent, is characterized by the fact that the continuity equation does not include any dispersive term. The Boussinesq equation system is numerically solved by a hybrid finite volume-finite difference scheme. A high-order upwind weighted essentially non-oscillatory(WENO) finite volume scheme that involves an exact Riemann solver is implemented. The wave breaking is represented by discontinuities of the weak solution of the integral form of the non-linear shallow water equations(NSWE). On the basis of the shock-capturing high order WENO scheme a new procedure, for the computation of the structure of the solution of a Riemann problem associated with a wet/dry front, is proposed in order to simulate the run up hydrodynamics in swash zone. The capacity of the proposed model to correctly represent wave propagation, wave breaking, run up and wave induced currents is verified against test cases present in literature. The results obtained are compared with experimental measures, analytical solutions or alternative numerical solutions. The proposed model is applied to a real case regarding the simulation of wave fields and nearshore currents in the coastal region opposite San Mauro Cilento(Italy).     

LARGE EDDY SIMULATION FOR PLUNGING BREAKER WAVE

1 .　INTRODUCTIONInthenear shoreregion ,aswavespropagateintoshallowwater ,theprocessofshoalingleadstotheincreaseofwaveheight ,however ,thisprocesscannotcontinue ,andatacertain positionthewavebreaks .Inpractice ,breakingwavesarepow erfulagentsforgeneratingturbulence ,whichplaysanimportantroleinmostofthefluiddynamicalprocessesthroughoutthesurfzone ,suchaswavetransformation ,generationofnear shorecurrent ,diffusionofmaterials ,andsedimenttransporta tion .Manynumericalstudieshavebeenconductedt…     

“网河”非稳定流模型在洪泛区洪流演进中的应用

将宽阔的溃口洪水行进范围概化成由河道水塘和联系河道组成的网河,用一维非恒定流方程组来描述主要的水充运动状态,通过简化和变换,改写成统一的四点线性隐式有限差的方程组形式,再用双消除法求解,全部计算在微机上实现,参数用实测资料率定,成果具有较好的精度,在一定程度上反映出横水流方向的水位流量变化,为防洪水利计算开辟一条新的途径。     

Modelling of 2-D extended Boussinesq equations using a hybrid numerical scheme

In this paper, a hybrid finite-difference and finite-volume numerical scheme is developed to solve the 2-D Boussinesq equations. The governing equations are the extended version of Madsen and Sorensen＇s formulations. The governing equations are firstly rearranged into a conservative form. The finite volume method with the HLLC Riemann solver is used to discretize the flux term while the remaining terms are discretized by using the finite difference method. The fourth order MUSCL-TVD scheme is employed to reconstruct the variables at the left and right states of the cell interface. The time marching is performed by using the explicit second-order MUSCL-Hancock scheme with the adaptive time step. The developed model is validated against various experimental measurements for wave propagation, breaking and runup on three dimensional bathymetries.     

A new three-dimensional finite-volume non-hydrostatic shock-capturing model for free surface flow

In this paper a new finite-volume non-hydrostatic and shock-capturing three-dimensional model for the simulation of wave-structure interaction and hydrodynamic phenomena(wave refraction, diffraction, shoaling and breaking) is proposed. The model is based on an integral formulation of the Navier-Stokes equations which are solved on a time dependent coordinate system: a coordinate transformation maps the varying coordinates in the physical domain to a uniform transformed space. The equations of motion are discretized by means of a finite-volume shock-capturing numerical procedure based on high order WENO reconstructions. The solution procedure for the equations of motion uses a third order accurate Runge-Kutta(SSPRK) fractional-step method and applies a pressure corrector formulation in order to obtain a divergence-free velocity field at each stage. The proposed model is validated against several benchmark test cases.     

综合考虑多种变形因素的近岸多向不规则波传播数学模型-I.模型的建立

根据线性波动的叠加原理和波浪方向谱理论,作者在综合考虑环境水流(水流因子)、非线性弥散影响(非线性因子)、底摩擦波能损失(底摩擦因子)、非缓坡地形影响(地形因子)、折射、绕射的近岸规则波传播基本方程的基础上,推导出了综合考虑多种变形因素的近岸多向不规则波传播变形的基本方程。使用有限差分作为数值方法,给出了波浪破碎和障碍物后边界的处理方法,建立了综合考虑环境水流(水流因子)、非线性弥散影响(非线性因子)、底摩擦波能损失(底摩擦因子)、非缓坡地形影响(地形因子)、折射、绕射、波浪破碎、障碍物影响的近岸多向不规则波传播变形数学模型。该模型以组成波的谱值及波向为变量,在实数域内求解,适合大面积海区波场计算。     

NUMERICAL SIMULATION OF PROPAGATION AND BREAKING PROCESSES OF A FOCUSED WAVES GROUP

A two-dimensional numerical wave flume is developed to study the focused waves group propagation and the consequent breaking processes. The numerical model is based on the Reynolds-Averaged Navier-Stokes (RANS) equations, with the standard k-ε turbulence model to simulate the turbulence effects. To track the complicated and broken free-surface, the Volume Of Fluid (VOF) method is employed. The numerical model combines the "Partial Cell Treatment (PCT)" method with the "Locally Relative Stationary (LRS)" concept to treat the moving wave paddle so that various waves can be generated directly in a fixed Cartesian grid system. The theoretical results of the linear and nonlinear waves are used to validate the numerical wave flume firstly, and then a plunging breaking wave created by a focused waves group is simulated. The numerical results are compared to the experimental data and other simulation results, with very good agreements. The turbulence intensity, the flow field and the energy dissipation in the breaking processes are analyzed based on the numerical results. It is shown that the present numerical model is efficient and accurate for studying the waves group generation, the waves packet propagation, and the wave breaking processes.     

A TVD-WAF-based hybrid finite volume and finite difference scheme for nonlinearly dispersive wave equations

A total variation diminishing-weighted average flux(TVD-WAF)-based hybrid numerical scheme for the enhanced version of nonlinearly dispersive Boussinesq-type equations was developed. The one-dimensional governing equations were rewritten in the conservative form and then discretized on a uniform grid. The finite volume method was used to discretize the flux term while the remaining terms were approximated with the finite difference method. The second-order TVD-WAF method was employed in conjunction with the Harten-Lax-van Leer(HLL) Riemann solver to calculate the numerical flux, and the variables at the cell interface for the local Riemann problem were reconstructed via the fourthorder monotone upstream-centered scheme for conservation laws(MUSCL). The time marching scheme based on the third-order TVD RungeKutta method was used to obtain numerical solutions. The model was validated through a series of numerical tests, in which wave breaking and a moving shoreline were treated. The good agreement between the computed results, documented analytical solutions, and experimental data demonstrates the correct discretization of the governing equations and high accuracy of the proposed scheme, and also conforms the advantages of the proposed shock-capturing scheme for the enhanced version of the Boussinesq model, including the convenience in the treatment of wave breaking and moving shorelines and without the need for a numerical filter.