带窄缝多箱体系统波浪荷载特性分析EI北大核心CSCD

针对波浪与带有窄缝多固定直角箱体结构作用产生的流体共振问题,建立了非线性波浪荷载分析二维时域模型。该模型采用域内源造波技术产生入射波浪,自由水面满足完全非线性运动学和动力学边界条件,窄缝内自由水面引入人工阻尼来等效由于涡旋运动和流动分离引起的粘性耗散,建立边界积分方程并采用高阶边界元离散求解物面上速度势等未知量,进而利用加速度势的方法来求得速度势时间导数,并基于伯努利方程积分得到作用结构上的瞬时波浪荷载。通过模拟带两窄缝的三箱体所受水平力与垂向力,并与已发表结果对比验证了模型的准确性。同时通过大量的数值计算,分析了箱体数量对各箱体所受波浪荷载大小及变化规律的影响。     

基于波浪-多孔介质海床-结构物耦合模型的单桩基础波浪力分析

为了研究波浪作用下多孔介质海床特性和结构物埋深及施工下放速度等因素对结构物所受波浪力的影响,采用修正RANS方程和Forchheimer饱和阻力模型控制流体流动,流体体积法（VOF）追踪自由液面,并采用κ-ε闭合方程进行求解,建立波浪-多孔介质海床-结构物相互作用研究的三维耦合数值分析模型。首先,进行数值模型的验证分析,包含多孔介质海床对波浪传播的衰减效应,波浪作用下结构物周围湍流流动以及海床多孔特性条件下WAVE FORCES结构物所受波浪力。然后,进行结构物所受水平波浪力影响因素的参数分析,主要包含波浪条件,多孔介质海床特性及结构物特性三个方面。结果表明:将多孔介质海床简化为刚性不可渗固体而忽视海床多孔特性,会低估结构物所受的波浪力数值;大波高长周期波浪作用下,深水结构物所受波浪力较大;海床孔隙率、颗粒直径、海床厚度显著影响结构物所受波浪力;同时,结构物直径、截面形式、埋置深度及其施工下放速度v等结构物特性对波浪力的影响同样显著。因此,工程实践中,应同时考虑波浪条件、多孔海床特性和结构物埋置深度及动态运动过程,合理计算结构物所受波浪力数值,以指导结构设计和施工。     

超大型结构物受波浪力作用的数值模拟

为了计算波浪效应下超大型结构物所受的波浪力,该文运用σ坐标变换来追踪随时间变化的自由液面,添加了浸没边界法(IBM)来处理不规则结构物表面,建立了基于大涡模拟(LES)方法的三维数值模型。为验证该数值模型的正确定,运用该模型来模拟规则波作用下大直径垂直圆柱的绕射问题,圆柱周围的波浪爬高数值解与解析解吻合良好。运用该三维数值模型,模拟了波浪与南京长江三桥南塔钢套箱相互作用的问题,数值计算出的结构物所受的波浪力与试验数据吻合良好,表明该数值模型能够很好地模拟工程中三维波浪与超大型结构物相互作用的问题。     

孤立波作用下圆柱桩波浪力计算方法研究EI北大核心CSCD

为研究孤立波作用下跨海桥梁桥墩受到的波浪荷载以得到孤立波波浪力的简化计算方法,利用计算流体力学软件OpenFOAM模拟海洋孤立波,在不同来流波高和初始水深下,开展了2组仿真试验,三维数值模拟用于直接计算圆柱体上的波浪力,二维数值模拟用于推导Morison方程所需的速度场。对比现有文献,讨论原始Morison方程应用于孤立波波浪力计算的适用性以及孤立波非线性的变化规律,并验证了引入非线性项的修正Morison方程预测孤立波荷载的适用性。研究结果表明:在计算孤立波荷载时,非线性影响不可忽视,随着波高和水深的比值H/d的增大,孤立波的非线性越来越强;相比原始Morison方程,考虑非线性影响的修正Morison方程可以更准确地预测孤立波与圆柱桩间的相互作用;应用修正Morison方程进行孤立波荷载预测时,波浪力参数C D,C M的取值与波高H、水深d、圆柱桩直径D的绝对值无关,仅与H/d有关;基于多组仿真试验结果,给出了0.15≤H/d≤0.65内波浪力参数的取值,可为孤立波荷载的快速计算提供参考。     

极端波浪作用下跨海箱形桥梁上部结构流固耦合特性研究EI北大核心CSCD

跨海桥梁面临着海洋环境中极端波浪的巨大威胁,波浪-结构的耦合作用特性是跨海箱形桥梁上部结构的极端波浪设计中需考虑的关键问题。采用OpenFOAM程序基于有限体积法离散不可压缩流体的Naiver-Stokes方程,并结合SST k-ω湍流模型模拟极端波浪的生成、传播及冲击作用,以弹簧-质量-阻尼系统模拟箱梁上部结构运动体系,并基于动网格方法构建极端波浪与箱梁上部结构相互作用的多相流耦合模型。通过与模型水槽试验结果和已有文献的仿真结果的对比验证该耦合模型的有效性,随后利用该耦合模型探究了波浪参数、结构特性及约束刚度等参数对箱形桥梁上部结构波浪荷载、动力特性及支座力的影响规律。结果表明:结构与流体的耦合效应导致箱形桥梁上部结构所受波浪荷载的波动增大和极值减小,其中水平波浪力最大降低28%,竖向波浪力最大降低22.5%,考虑流固耦合能更为合理地反映极端波浪作用下跨海箱形桥梁上部结构的实际波浪荷载;随着结构自振周期的增大,箱形桥梁上部结构所受的水平弹簧约束刚度下降,进而导致箱形桥梁上部结构的水平位移增大;在跨海桥梁上部结构的支座设计中不仅需要考虑上部结构所受波浪荷载,还应考虑结构运动及流固耦合效应对支座力的影响。     

基于Pasternak海床模型的椭圆余弦波浪荷载作用下埋置管线动力响应解析解

通过两阶段分析方法，针对椭圆余弦波作用下埋置管线的动力响应进行了探究。基于椭圆余弦波理论，采用Biot固结方程推导了非线性波浪作用下浅水区埋置管线所受的周期波浪压力；将管线考虑为动力Pasternak海床模型上的Euler-Bernoulli梁，将波浪动荷载施加到管线上获得无限长管线的动力响应偏微分控制方程；利用Fourier变换和Laplace变换并借助卷积定理得到管线挠度、速度、加速度、转角、弯矩和剪力的动力响应解。通过与三维有限元数值算例及既有试验结果对比验证了解析解的正确性与适用性。对椭圆余弦波作用下埋置管线的动力响应特性进行了敏感参数分析，结果表明：波浪高度H显著影响了波面形状与海床内波浪力大小，不同浪高下管线转角、弯矩和剪力的变化更明显，而挠度、速度和加速度响应敏感性则较低。     

匀加速激励下的液体晃动力解析计算

针对矩形容器在匀加速运动下的液体晃动问题,采用基于非线性振动的解析方法求出容器所受液体晃动力的解析近似解,并分析其非线性效应以及加速度大小和充液率的影响作用。根据流体速度势的解析解计算边壁处的流体压力,而对于部分边壁区域的流体压力则采用线性分布的近似估计。对流体压力沿边壁做积分即可获得边壁处液体晃动力的解析近似解。计算结果表明,非线性因素并不会对容器所受晃动力产生较大影响,晃动力非线性项与加速度立方成正比;充液率的变化会使得线性晃动固有频率的数值发生改变,进而对晃动力线性项造成影响,其影响程度与固有频率曲线的变化趋势较为一致。     

复式防波堤断面尺度对波浪爬高的影响研究

数值模拟是求解防波堤爬高问题的重要方法。以Navier-Stokes方程为控制方程,该文建立了基于紧致插值曲线法(CIP法)的二维不可压缩流体的有限差分数值模型。通过分步算法对时间积分求解控制域,采用双曲正切函数自由面捕捉法(THINC法)对自由液面进行捕捉,采用浸入边界法IBM对固体边界进行处理,将波浪爬高问题视为固-液-气多相流问题。通过建立二维数值水槽,对波浪爬高越浪问题进行数值验证;进而在相同波浪条件下,对不同断面尺寸的复式防波堤进行波浪爬高的数值模拟。结果表明:该模型可以较好地模拟波浪过程中的变形、翻卷、破碎等强非线性现象,得出最大爬高与复式防波堤尺寸之间的关系,从而给出了最小爬高时对应的防波堤断面尺度。     

求解三维物体波浪荷载的边界元模型

建立了求解规则波中任意形状三维物体绕射问题的边界元模型。设置辐射面将流场分为内、外场,外场中的绕射势用特征函数展开式解析表达,内场则由边界积分方程求解,所取的Green 函数为简单的1/r 形式。内场边界采用四边形面元和轴对称面元混合布置的划分方式,轴对称面元上奇点强度沿周向为Fourier 级数展开的高次分布,提高了求解三维绕射问题的精度和效率。经与直立圆柱绕射的线性理论解比较,验证了数值方法的可靠性。利用谱分析原理,将规则波中的结果拓展,得到多向不规则波中绕射物体所受波浪力的统计特性。     

箱形船体波浪和波浪压力的非线性时域模型

该文将耦合计算模型应用于计算固定箱形船体上非线性波浪压力,研究了将该准三维模型应用于物体三维波浪压力的计算能力.为了提高计算强非线性波浪的能力,在方程中加入了高阶非线性项,并进行了箱体波浪压力的测量模型实验,以验证计算结果.计算模型将船体底面以下水域取为内域,其余水域为外域.内域用欧拉方程计算,外域采用Boussine...     

Nonlinear wave propagation and run-up generated by subaerial landslides modeled using meshless method

The focus of present study is on water waves generated by landslides. Because such problems involve moving boundaries and large deformation of the computational domain, a 2-D numerical model is established with a meshless method and a fully nonlinear Lagrangian time marching scheme. The method chosen in this study is a RBF collocation method developed in the way that the collocations of both the governing equation and boundary conditions are applied at each of the boundary points. This guarantees the accuracies of the partial derivatives of the velocity potential near the free surface, which results in the precise prediction of the free surface. A very effective treatment is proposed for the landslide boundary in this study. Present model is verified by comparing the numerical results of waves generated by a submerged landslide with other numerical solutions, including those obtained using the BIEM and Boussinesq-type models. Fairly good agreements are observed. Present model is then applied to simulate subaerial landslide-induced waves. Various slopes are considered. The landslide-induced wave propagation and shoreline motions are examined. The effects of sliding horizontal distance along a given slope on the induced wave are also discussed.     

Numerical modeling of wave breaking induced by fixed or moving boundaries

In this paper, several numerical aspects of an existing model for fully nonlinear waves are improved and validated to study wave breaking due to shoaling over a gentle plane slope and wave breaking induced by a moving lateral boundary.The model is based on fully nonlinear potential flow theory and combines a higher-order Boundary Element Method (BEM) for solving Laplace's equation at a given time and Lagrangian Taylor expansions for the time updating of the free surface position and potential. An improved numerical treatment of the boundary conditions at the intersection between moving lateral boundaries and the free surface (corner) is implemented and tested in the model, and the free surface interpolation method is also improved to better model highly curved regions of the free surface that occur in breaking waves. Finally, a node regridding technique is introduced to improve the resolution of the solution close to moving boundaries and in breaker jets.Examples are presented for solitary wave propagation, shoaling, and breaking over a 1:35 slope and for wave breaking induced by a moving vertical boundary. Using the new methods, both resolution and extent of computations are significantly improved compared to the earlier model, for similar computational efforts. In all cases computations can be carried out up to impact of the breaker jets on the free surface.     

Applicability of the method of fundamental solutions to 3-D wave–body interaction with fully nonlinear free surface

A numerical model for three-dimensional fully nonlinear free-surface waves is developed by applying a boundary-type meshless approach with a leap-frog time-marching scheme. Adopting Gaussian Radial Basis Functions to fit the free surface, a non-iterative approach to discretize the nonlinear free-surface boundary is formulated. Using the fundamental solutions of the Laplace equation as the solution form of the velocity potential, free-surface wave problems can be solved by collocations at only a few boundary points since the governing equation is automatically satisfied. The accuracy of the present method is verified by comparing the simulated propagation of a solitary wave with an exact solution. The applicability of the present model is illustrated by applying it to the problem of a solitary wave running up on a vertical surface-piercing cylinder and the problem of wave generation in infinite water depth by a submerged moving object.     

Corner problems and global accuracy in the boundary element solution of nonlinear wave flows

The numerical model for nonlinear wave propagation in the physical space, developed by Grilli, et al.^12,13, uses a higher-order BEM for solving Laplace's equation, and a higher-order Taylor expansion for integrating in time the two nonlinear free surface boundary conditions. The corners of the fluid domain were modelled by double-nodes with imposition of potential continuity. Nonlinear wave generation, propagation and runup on slopes were successfully studied with this model. In some applications, however, the solution was found to be somewhat inaccurate in the corners and this sometimes led to wave instability after propagation in time.

In this paper, global and local accuracy of the model are improved by using a more stable free surface representation based on quasi-spline elements and an improved corner solution combining the enforcement of compatibility relationships in the double-nodes with an adaptive integration which provides almost arbitrary accuracy in the BEM numerical integrations. These improvements of the model are systematically checked on simple examples with analytical solutions. Effects of accuracy of the numerical integrations, convergence with refined discretization, domain aspect ratio in relation with horizontal and vertical grid steps, are separately assessed. Global accuracy of the computations with the new corner solution is studied by solving nonlinear water wave flows in a two-dimensional numerical wavetank. The optimum relationship between space and time discretization in the model is derived from these computations and expressed as an optimum Courant number of 0.5. Applications with both exact constant shape waves (solitary waves) and overturning waves generated by a piston wavemaker are presented in detail.     

液体非线性晃动的同步Hopf分叉现象

针对受俯仰激励作用的圆柱形贮箱中液体非线性晃动,用变分原理建立了液体晃动的压力体积分形式的Lagrange函数;并将速度势函数在自由液面处作波高函数的级数展开,从而导出自由液面运动学和动力学边界条件非线性方程组;最后用四阶Runge-Kutta法求解非线性方程组。计算发现,在一定的激励频率内面外主模态和次生模态发生同步Hopf分叉,并给出了发生分叉的频率区域。     

Local and global properties of the harmonic polynomial cell method: In‐depth analysis in two dimensions

A detailed and systematic analysis is performed on the local and global properties of the recently developed harmonic polynomial cell (HPC) method, a very accurate and efficient field solver for problems governed by the Laplace equation. At the local cell level, a simple rule is identified for the proper choice of harmonic polynomials in the local representation of the velocity potential in cells with symmetry properties. The local solution error, its convergence rate, its dependence on the cell topology, its distribution inside the cell, and its features across cells with different dimensions are carefully examined with relevant findings for HPC numerical implementations. At the global level, the error convergence rate is analytically estimated in terms of error contributions from the boundary conditions and from inside the liquid domain. In most cases, the error associated with boundary conditions dominates the global error. In order to minimize it, Quadtree grid strategies or high‐order local expressions of the velocity potential are proposed for cells near critical boundary portions. To model accurately the boundary conditions on rigid or deformable surfaces with generic geometries, 3 different grid strategies are proposed by adopting concepts of immersed boundary method and overlapping grids. They are comparatively studied for a circular rigid cylinder in infinite fluid and for the propagation of a free‐surface wave. Then, an immersed boundary strategy, using numerical choices suggested in this paper, is successfully compared against a fully nonlinear boundary element method for the case of a surface‐piercing circular cylinder heaving in otherwise calm water.     

Free‐surface tracking in 2D with the harmonic polynomial cell method: Two alternative strategies

Several cases of nonlinear wave propagation are studied numerically in two dimensions within the framework of potential flow. The Laplace equation is solved with the harmonic polynomial cell (HPC) method, which is a field method with high‐order accuracy. In the HPC method, the computational domain is divided into overlapping cells. Within each cell, the velocity potential is represented by a sum of harmonic polynomials. Two different methods denoted as immersed boundary (IB) and multigrid (MG) are used to track the free surface. The former treats the free surface as an IB in a fixed Cartesian background grid, while the latter uses a free‐surface fitted grid that overlaps with a Cartesian background grid. The simulated cases include several nonlinear wave mechanisms, such as high steepness and shallow‐water effects. For one of the cases, a numerical scheme to suppress local wave breaking is introduced. Such scheme can serve as a practical mean to ensure numerical stability in simulations where local breaking is not significant for the result. For all the considered cases, both the IB and MG method generally give satisfactory agreement with known reference results. Although the two free‐surface tracking methods mostly have similar performance, some differences between them are pointed out. These include aspects related to modeling of particular physical problems as well as their computational efficiency when combined with the HPC method.     

The boundary element method applied to the analysis of two-dimensional nonlinear sloshing problems

This paper deals with an application of the boundary element method to the analysis of nonlinear sloshing problems, namely nonlinear oscillations of a liquid in a container subjected to forced oscillations. First, the problem is formulated mathematically as a nonlinear initial-boundary value problem by the use of a governing differential equation and boundary conditions, assuming the fluid to be inviscid and incompressible and the flow to be irrotational. Next, the governing equation (Laplace equation) and boundary conditions, except the dynamic boundary condition on the free surface, are transformed into an integral equation by employing the Galerkin method. Two dynamic boundary condition is reduced to a weighted residual equation by employing the Galerkin method. Two equations thus obtained are discretized by the use of the finite element method spacewise and the finite difference method timewise. Collocation method is employed for the discretization of the integral equation. Due to the nonlinearity of the problem, the incremental method is used for the numerical analysis. Numerical results obtained by the present boundary element method are compared with those obtained by the conventional finite element method and also with existing analytical solutions of the nonlinear theory. Good agreements are obtained, and this indicates the availability of the boundary element method as a numerical technique for nonlinear free surface fluid problems.     

深水铰接塔平台的非线性动力特性分析

研究了铰接塔平台在波浪和海流作用下的非线性动力特性。将平台顶部工作单元简化为集中质量,塔柱和浮力仓简化为均匀直杆,建立了铰接塔平台动力分析模型。考虑海流和波浪对平台的作用,应用Morison公式计算铰接塔平台瞬时位置所受水动力,依据拉格朗日原理建立了铰接塔平台的强非线性运动方程。分别考虑波浪作用和波流联合作用,采用数值计算的方法研究了铰接塔平台超谐共振和混沌运动。研究表明,波流联合作用下平台的超谐共振运动响应增加,在大幅和较高频率波浪激励下,平台系统出现混沌运动。