港湾三维水动力和污染物扩散数值模型

本文提出一种浅海三维污染物扩散数值模拟的方法。首先建立σ坐标系下的Navier-Stoker方程及物质扩散方程。基于过程分裂法将前者分解为外模式（二维方程组）及内模式（三维方程组）；并且引入窄缝法对变边界进行模拟，由此建立三维σ坐标潮流模型；并找到σ坐标系下三维污染物扩散方程的差分方法，最后建立三维σ坐标污染物扩散模型。本模型已被应用于厦门海域，并对其2002年海水水质（CODCr值增量)进行了预测。应用结果表明，这种三维可变边界污染物扩散数值模型能够较好地对具有较大面积浅海滩涂的海区进行水质模拟和预测。     

河口海岸三维双σ坐标斜压水流数值模型研究

在海底地形陡变、垂向密度分层明显的水域,三维σ坐标模式中会出现一种"伪"水平斜压梯度力,并会引起"伪"密度流,以至于影响模拟的精度。垂向上引入双σ坐标变换,建立河口海岸水域三维斜压水流数值模型。数值试验结果表明,在海底地形陡变水域,双σ坐标模式可以减小水平斜压梯度力处理引起的误差。     

河口海岸三维水流数值模型中几种垂向坐标模式研究述评

回顾了近年来国内外河口、近岸海域三维斜压水流数值模式研究的进展,着重讨论了不同垂向坐标下三维水流模式的发展状况以及存在的问题。地形拟合坐标(σ坐标)模式可以很好地拟合床面地形和自由面,已在物理海洋学中被广泛使用。但在地形变化剧烈,尤其在密度层结效应明显的海域,σ坐标模式中的水平压强梯度力误差会引起伪密度流。寻求高精度的数值模式以及更加有效的拟合坐标变换将是值得努力的方向。     

胶州湾三维变动边界的潮流数值模拟

基于Blumberg等（1986）的河口、陆架和海洋模式，引入变边界处理技术，建立了胶州湾三维变动边界的潮流模型，模型以σ-正交曲线坐标下三维非线性潮波方程为基本方程，引入2.5阶瑞封闭方程组，采用分裂算子法数值求解方程组，利用湍封闭方程求解垂直紊动粘滞系数，采用干湿网格方法模拟潮流漫滩过程，三维变动边界潮流模型计算结果与实测值吻合良好。     

海岸三维潮流数学模型的研究及应用

本模型以三维Navier－Stokes方程为基础,经σ-坐标变换得模式方程,然后选用特殊的插值函数,利用有限元和差分相结合的方法求解.所建模型可适应具有较为复杂岸线和海工建筑的海域潮流计算,可进行局部加密,同时能以较高分辨率揭示三维潮流的空间结构特征.本潮流模型具有省时、简便的特点.     

长江口正压、斜压诊断及斜压预报模式--三维流场数值模拟

建立了σ坐标系下长江口正压、斜压诊断及斜压预报模式三维流场数学模型,采用k-kl二方程紊流闭合模型求解垂向涡粘系数。通过正压模式与斜压诊断模式、斜压诊断模式与斜压预报模式流场模拟结果的定量比较,说明了各种模式对长江口流场模拟精度影响的程度,推荐了长江口流场数值模拟采用的模式。     

渤海三维潮流数值模拟

本模型以具有自由面的三维非线性Ｎａｖｉｅｒ－Ｓｒｏｋｅｓ方程为基本方程，经σ坐标变换得到模式方程。基于过程分裂法，将三维流动中的快过程与慢过程劈开，并对每部分选用适合其物理特性和数值行为的计算格式，然后耦联求解。应用本模型详细计算了渤海的三维潮运动。其中，潮波系统模拟获得理想的结果；采用十层模式计算了Ｍ２潮流，以较高的辨率揭示了潮流的空间结构特征。最后本文给出了三维潮流预报的应用实例。     

一种二维和三维嵌套海洋流体动力学数值模式及其在北部湾潮汐和潮流数值模拟中的应用

研究设计了一种二维和三维嵌套、外模态和内模态分离的水动力学数值模式,既可用于潮汐,也可用于风暴潮的数值计算。该模型对全部海区进行二维计算,对其中重点关心的海区同时进行三维计算。在三维计算区域,采用了内、外模态既分离又耦合的计算技术。数值格式采用全部交错的网格结构,三维模型中垂直方向采用σ-坐标代替通常的z-坐标,垂直涡动粘性系数由混合长度理论确定,垂直粘性项采用隐式差分格式。作为算例,本文对南海北部湾潮波进行了细网格的数值计算。     

太湖台风风暴流准三维数值模拟的应用

本文应用丁氏圆形台风模式，建立了太湖台风风暴流场的准三维数值模式，模型考虑了垂向涡粘系数沿水深变化和动量方程的修正，在对9711号（Winnie)台风影响下太湖各站水位验证的基础上，对太湖台风风暴流场进行了模拟计算。结果表明，该模式可对湖泊的台风风暴流进行复演和预测计算。从预测研究的角度看，基于台风模式的湖泊台风风暴流计算模式更有价值。     

海岸工程中实用三维流场数学模型研究

本文以完整的具有自由表面的三维非线性Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程组为基础方程，经垂向σ坐标变换后得到模型方程。采用有限差分法进行数值求解；垂向上等间距分层，使用隐式中心差分格式；水平方向上给出两套网格－正方网格和不规则三角形网格离散形式。     

Quasi-3D Numerical Simulation of Tidal Hydrodynamic Field

Based on the 2D horizontal plane numerical model,a quasi-3D numerical model is establishedfor coastal regions of shallow water.The characteristics of this model are that the velocity profiles can be ob-tained at the same time when the equations of the value of difference between the horizontal current velocityand its depth-averaged velocity in the vertical direction are solved and the results obtained are consistent withthe results of the 2D model.The circulating flow in the rectangular area induced by wind is simulated and ap-plied to the tidal flow field of the radial sandbanks in the South Yellow Sea.The computational results fromthis quasi-3D model are in good agreement with analytical results and observed data.The solution of the finitedifference equations has been found to be stable,and the model is simple,effective and practical.     

Conjunction of 2D and 3D modified flow solvers for simulating spatio-temporal wind induced hydrodynamics in the Caspian Sea

The main objective of this study is the simulation of flow dynamics in the deep parts of the Caspian Sea, in which the southern and middle deep regions are surrounded by considerable areas of shallow zones. To simulate spatio-temporal wind induced hydrodynamics in deep waters, a conjunctive numerical model consisting of a 2D depth average model and a 3D pseudo compressible model is proposed. The 2D model is applied to determine time dependent free surface oscillations as well as the surface velocity patterns and is conjunct to the 3D flow solver for computing three-dimensional velocity and pressure fields which coverage to steady state for the top boundary condition. The modified 2D and 3D sets of equations are conjunct considering interface shear stresses. Both sets of 2D and 3D equations are solved on unstructured triangular and tetrahedral meshes using the Galerkin Finite Volume Method. The conjunctive model is utilized to investigate the deep currents affected by wind, Coriolis forces and the river inflow conditions of the Caspian Sea. In this study, the simulation of flow field due to major winds as well as transient winds in the Caspian Sea during a period of 6 hours in the winter season has been conducted and the numerical results for water surface level are then compared to the 2D numerical results.     

Mud mass transport due to waves based on an empirical rheology model featured by hysteresis loop

A vertical 2-D water–mud numerical model is developed for estimating the rate of mud mass transport under wave action. A nonlinear semi-empirical rheology model featured by remarkable hysteresis loops in the relationships of the shear stress versus both the shear strain and the rate of shear strain of mud is applied to this water–mud model. A logarithmic grid in the vertical direction is employed for numerical treatment, which increases the resolution of the flow in the neighborhood of both sides of the interface. Model verifications are given through comparisons between the calculated and the measured mud mass transport velocities as well as wave height changes.     

Numerical Modeling of Water Wave Interaction with A Soft Mud Bed

A vertical 2-D numerical model is presented for simulating the interaction between water waves and a soft mud bed. Taking into aceotmt nonlinear theology, a semi-empirical theological model is applied to this water-mud model, reflecting the combined visco-elasto-plastic properties of soft mud under such oscillatory external forces as water waves. In order to increase the resolution of the flow in the neighborhood of both sides of the inter-surface, a logarithmic grid in the vertical direction is employed for numerical treatment. Model verifications are given through comparisons between the calculated and the measured mud mass transport velocities as well as wave height changes.     

Numerical study on the flow characteristics of tidal jets induced by a tidal-jet-generator

The flow characteristics of tidal jets induced by a Tidal-Jet Generator (TJG) are investigated using a finite-difference numerical scheme, named Navier–Stokes (NS)–Marker and Cell (MAC)-TIDE, based on the fully 3D NS equations. The TJG is an enclosed rectangular breakwater, which has vertical opening and a large enclosed volume inside. During both phases of tide, strong and uni-directional jets can be obtained locally from the inlet of the TJG, due to the water level difference between the inner and outer sides of TJG.The computed results are extensively compared with three other independently developed numerical models; 3D-ADI, DVM, and CIP-CSF. These models are based on quasi-3D, 2D depth-averaged, and fully 3D NS equations, respectively. It is seen that the present fully 3D numerical model NS–MAC-TIDE can predict the maximum intensity of inlet velocity with higher accuracy than the other numerical models when compared with the empirical function proposed from the experiments. The numerical simulations based on NS–MAC-TIDE can reproduce successfully the processes of generation, development, and dissipation of tidal jets. The effects of gap opening on the main characteristics of the tidal jet flow are assessed. Through numerical assessment, it is also clearly demonstrated that the residual time of a pollutant distributed around the front of the TJG can be decreased by significant amount due to the locally induced tidal jet. The TJG can thus utilize tidal energy for water purification in local marine environment by providing a flushing mechanism.     

A Numerical Investigation of the Reduction of Solitary Wave Runup by A Row of Vertical Slotted Piles

To improve the current understanding of the reduction of tsunami-like solitary wave runup by the pile breakwater on a sloping beach, we developed a 3D numerical wave tank based on the CFD tool OpenFOAM in this study. The Navier Stokes equations were applied to solve the two-phase incompressible flow, combined with an LES model to solve the turbulence and a VOF method to capture the free surface. The adopted model was firstly validated with existing empirical formulas for solitary wave runup on the slope without the pile structure. It is then validated using our new laboratory observations of the free surface elevation, the velocity and the pressure around a row of vertical slotted piles subjected to solitary waves, as well as the wave runup on the slope behind the piles. Subsequently, a set of numerical simulations were implemented to analyze the wave reflection, the wave transmission, and the shoreline runup with various offshore wave heights, offshore water depths, adjacent pile spaces and beach slopes. Finally, an improved empirical equation accounting for the maximum wave runup on the slope was proposed by taking the presence of the pile breakwater into consideration.     

Three-dimensional liquid sloshing in a tank with baffles

A numerical model has been developed to study three-dimensional (3D) liquid sloshing in a tank with baffles. The numerical model solves the spatially averaged Navier-Stokes equations, which are constructed on a non-inertial reference frame having six degree-of-freedom (DOF) of motions. The large-eddy-simulation (LES) approach is employed to model turbulence by using the Smagorinsky sub-grid scale (SGS) closure model. The two-step projection method is employed in the numerical solutions, aided by the Bi-CGSTAB technique to solve the pressure Poisson equation for the filtered pressure field. The second-order accurate volume-of-fluid (VOF) method is used to track the distorted and broken free surface. The baffles in the tank are modeled by the concept of virtual boundary force (VBF) method. The numerical model is first validated against the available analytical solution and experimental data for two-dimensional (2D) liquid sloshing in a tank without baffles. The 2D liquid sloshing in tanks with baffles is then investigated. The numerical results are compared with other results from available literatures. Good agreement is obtained. Finally, the model is used to study 3D liquid sloshing in a tank with vertical baffles. The effect of the baffle is investigated and discussed.     

A Study of Eddy Viscosity Coefficient in Numerical Tidal Simulation

Based on the fluid motion equations, the physical meaning of eddy viscosity coefficient and the rationality of the Boussinesq hypothesis are discussed in this paper. The effect of the coefficient on numerical stability is analyzed briefly. A semi-enclosed rectangular sea area, with an orthogonal spur dike, is applied in a 2-D numerical model to study the effect of horizontal eddy viscosity coefficient (AH). The computed result shows that AH has little influence on the tidal level and averaged flow velocity, but has obvious influence on the intensity and the range of return flow around near the spur dike. Correspondingly, a wind-driven current pool and an annular current are applied in a 3-D numerical model respectively to study the effect of vertical eddy viscosity coefficient (Av). The computed result shows that the absolute value of Av is inversely proportional to that of horizontal velocity, and the vertical gradient value of Av determines the vertical distribution of horizontal velocity. The distrib     

Computation of Viscous Uniform and Shear Flow over A Circular Cylinder by A Finite Element Method

The incompressible viscous uniform and shear flow past a circular cylinder is studied. The two-dimensional Navier-Stokes equations are solved by a finite element method. The governing equations are discretized by a weighted residual method in space. The stable three-step scheme is applied to the momentum equations in the time integration. The numerical model is firstly applied to the computation of the lid-driven cavity flow for its validation. The computed results agree well with the measured data and other numerical results. Then, it is used to simulate the viscous uniform and shear flow over a circular cylinder for Reynolds numbers from lO0 to lO00. The transient time interval before the vortex shedding occurs is shortened considerably by introduction of artificial perturbation. The computed Strouhal number, drag and lift coefficients agree well with the experimental data. The computation shows that the finite element model can be successfully applied to the viscous flow problem.     

波浪与抛石潜堤相互作用的MPS法数值模型研究

为了研究波浪与抛石潜堤相互作用过程中大自由表面变形和堤内渗流等强非线性紊流运动问题,利用改进的MPS法,建立了模拟波浪与抛石潜堤相互作用的MPS法数值计算模型。模型将抛石潜堤假定为均质多孔介质,采用Drew的二相流运动方程描述多孔介质内外的流体运动;通过在动量方程中增加非线性阻力项,并引入亚粒子尺度紊流模型,模拟波浪与可渗结构物相互作用过程中的紊流运动。选取“U”型管中多孔介质内渗流过程和孤立波与可渗潜堤相互作用两个典型的渗流问题,通过将数值计算结果与理论解和实测值的对比分析,对所提出的MPS法紊流渗流模型的模拟精度进行验证。结果表明:基于改进的MPS法构建的垂向二维紊流渗流模型可以很好地再现“U”型管中多孔介质内渗流以及波浪作用下可渗潜堤内外的复杂流场,显著缓解流-固界面处的压力震荡与粒子分布不均匀问题,实现了较高的模拟精度。