A three-dimensional semi-implicit unstructured grid finite volume ocean model

A new three-dimensional semi-implicit finite-volume ocean model has been developed for simulating the coastal ocean circulation, which is based on the staggered C -unstructured non-orthogonal grid in the horizontal direction and z -level grid in the vertical direction. The three-dimensional model is discretized by the semi-implicit finite-volume method, in that the free-surface and the vertical diffusion are semi-implicit, thereby removing stability limitations associated with the surface gravity wave and vertical diffusion terms. The remaining terms in the momentum equations are discretized explicitly by an integral method. The partial cell method is used for resolving topography, which enables the model to better represent irregular topography. The model has been tested against analytical cases for wind and tidal oscillation circulation, and is applied to simulating the tidal flow in the Bohai Sea. The results are in good agreement both with the analytical solutions and measurement results.     

A new efficient finite volume modeling of small amplitude free surface flows with unstructured grid

A staggered finite-volume technique for non-hydrostatic, small amplitude free surface flow governed by the incompressible Navier-Stokes equations is presented there is a proper balance between accuracy and computing time. The advection and horizontal diffusion terms in the momentum equation are discretized by an integral interpolation method on the orthogonal unstructured staggered mesh and, while it has the attractive property of being conservative. The pressure-correction algorithm is employed for the non-hydrostatic pressure in order to achieve second-order temporal accuracy. A conservative scalar transport algorithm is also applied to discretize k-ε equations in this model. The eddy viscosity is calculated from the k-ε turbulent model. The resulting model is mass and momentum conservative. The model is verified by two examples to simulate unsteady small amplitude free surface flows where non-hydrostatic pressures have a considerable effect on the velocity field,and then applied to simulate the tidal flow in the Bohai Sea.     

A finite element model of circulation in shallow water with moving boundary on tidal-flat

To examine the circulation in shallow water with tidal flat, a finite element model for the numerical solution of the shallow water equations was developed by means of standard Galerkin's method. The domain computed was covered with triangular finite elements, and water elevation and velocity were approximated by linear interpolation functions, and the lumped coefficients were used to substitute for solving the high order algebraic equation system. The time-dependent land-water boundary changes are treated mathematically by interrelating the location of the land-water boundary with the instantaneous tidal level. The implicit scheme was adopted for the terms of the bottom friction and the Coriolis effect in the motion equation so that the numerical stability of the model has been improved.The model was applied to the tidal current on shoaling water with large tidal flat off Pikou, and a comparison between observed and calculated values showed good agreement, the flow pattern being reproduced. The result     

A Vertical Two-Dimensional Model to Simulate Tidal Hydrodynamics in A Branched Estuary

A vertical (laterally averaged) two-dimensional hydrodynamic model is developed for tides, tidal current, and salinity in a branched estuarine system. The goveming equations are solved with the hydrostatic pressure distribution assumption and the Boussinesq approximation. An explicit scheme is employed to solve the continuity equations. The momentum and mass balance equations are solved implicitly in the Cartesian coordinate system. The tributaries are govemed by the same dynamic equations. A control volume at the junctions is designed to conserve mass and volume transport in the finite difference schemes, based on the physical principle of continuum medium of fluid. Predictions by the developed model are compared with the analytic solutions of steady wind-driven circulatory flow and tidal flow. The model results for the velocities and water surface elevations coincide with analytic results. The model is then applied to the Tanshui River estuarine system. Detailed model calibration and verification have been conducted with measured water surface elevations,tidal current, and salinity distributions. The overall performance of the model is in qualitative agreement with the available field data. The calibrated and verified numerical model has been used to quantify the tidal prism and flushing rate in the Tanshui River-Tahan Stream, Hsintien Stream, and Keelung River.     

厦门海域浅水三维潮流场动力学模型

基于Casulli的三维浅水模型,改进浅滩处理方法,并入简化的紊流闭合模型,形成完整的海洋动力学基本方程组,改进了紊流闭合模型的求解方法,动力学模拟结果与实测结果符合良好,海域中大量浅滩的干出与淹没的面积和位置与实际情况吻合良好.本模型是厦门海域海洋动力学理论研究中第一个完全的三维斜压潮流场模型,全部程序用FORTRAN语言独立开发和编写.     

极浅海域潮流数值模型

通过对以往的浅水环流数值模型进行改进，建立适用于极浅水域的且能达到较高分辨率的潮汐环流数值模型。模型的主要特点是：（１）通过改进海底摩擦项的表达式来克服传统的二次方律在极浅的潮滩区所产生的不稳定问题；（２）采用逆风格式处理动量方程中的平流项，有效地抑制由于岸边界移动引起的数值短波的扩散。结合老虎滩湾海上工程的需要，利用本模型进行一系列的数值模拟试验。经过实测资料验证表明，改进后的模型具有良好的稳定     

An unstructured-grid, finite-volume, nonhydrostatic, parallel coastal ocean simulator

A finite-volume formulation is presented that solves the three-dimensional, nonhydrostatic Navier–Stokes equations with the Boussinesq approximation on an unstructured, staggered, z-level grid, with the goal of simulating nonhydrostatic processes in the coastal ocean with grid resolutions of tens of meters. In particular, the code has been developed to simulate the nonlinear, nonhydrostatic internal wave field in the littoral ocean. The method is based on the formulation developed by Casulli, in that the free-surface and vertical diffusion are semi-implicit, thereby removing stability limitations associated with the surface gravity wave and vertical diffusion terms. The remaining terms in the momentum equations are discretized explicitly with the second-order Adams–Bashforth method, while the pressure-correction method is employed for the nonhydrostatic pressure in order to achieve overall second-order temporal accuracy. Advection of momentum is accomplished with an Eulerian discretization which conserves momentum in cells that do not contain the free surface, and scalar advection is discretized in a way that ensures consistency with continuity, thereby ensuring local and global mass conservation using a velocity field that conserves volume on a local and global basis. The nonhydrostatic pressure field is solved efficiently using a block-Jacobi preconditioner, and while stability is limited by the internal gravity wave speed and vertical advection of momentum, applications requiring relatively small time steps due to accuracy or stability constraints are run efficiently on parallel computers, since the present formulation is written entirely with the message-passing interface (MPI). The ParMETIS libraries are employed in order to achieve a load-balanced parallel partitioning that minimizes interprocessor communication, and the grid is reordered to optimize per-processor performance by limiting cache misses while accessing arrays in memory. Test cases demonstrate the ability of the code to efficiently and accurately compute the nonhydrostatic lock exchange and internal waves in idealized as well as real domains, and we evaluate the parallel efficiency of the code using up to 32 processors.     

圆形数值波浪水池斜向和多向入射波浪模拟研究

为了研究斜向入射波浪,基于三维不可压缩两相流模型,开发了一套圆形数值波浪水池数值模型。在圆形波浪水池中,通过源项造波法成功生成了任意入射方向的波浪,并且利用人工摩擦项模拟阻尼区以数值耗散反射波浪。模型基于嵌入式多块网格体系,采用FVM法(finite volume method)离散Navier-Stokes方程,VOF法(volume of fluid)追踪自由水面。试验结果表明,斜向入射波浪的模拟结果与理论值基本一致,圆形波浪水池在模拟斜向入射波浪时,有效区域的面积较传统波浪水池显著增大,而且有效区域受波浪入射角度的影响也较小。同时,通过叠加多列斜向入射波浪,模拟出了多向交叉波列,并通过与理论结果对比,发现其具有较高的精度。     

An Efficient Hydrodynamic Model for Surface Waves

In the present study,a semi-implicit finite difference model for non-bydrostatic,free-surface flows is analyzed and discussed.The governing equations are the three-dimensional free-surface Reynolds-averaged Navier-Stokes equations defined on a general,irregular domain of arbitrary scale.At outflow,a combination of a sponge layer technique and a radiation boundary condition is applied to minimize wave reflection.The equations are solved with the fractional step method where the hydrostatic pressure component is determined first,while the non-hydrostatic component of the pressure is computed from the pressure Poisson equation in which the coefficient matrix is positive definite and symmetric.The advectiou and horizontal viscosity terms are discretized by use of a semi-Lagrangian approach.The resulting model is computationally efficient and unrestricted to the CFL condition.The developed model is verified against analytical solutions and experimental data,with excellent agreement.     

大规模多岛屿海域潮流场的数值模拟

本文提出了一种系统地分析大规模多岛屿海域潮流场的数值模拟方法,以及只有有限代表点位的计算区域内的潮汐和潮流资料的分析方法。建立了适用于复杂的多岛屿海域上平面二维潮波数值计算模型的选择及网格自动剖分方法。通过对长海县长山群岛海域潮流场的模拟,验证了此方法在计算规模大而又要求局部分辨率高的潮流场时,该方法效率高,经济合理,灵活方便。     

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。     

A Three-Dimensional Prediction Method for Thermal Diffusion

A three-dimensional,first order turbulence closure,thermal diffusion model is described inthis paper.The governing equations consist of an equation of continuity,three components of momentum,conservation equations for salt,temperature and subgridscale energy,and an equation of state.In the mod-el,according to the hypothesis of Kolmogorov and Prandtl,the viscosity coefficient of turbulent flow ofhomogeneous fluid is related to the local turbulent energy,and the horizontal and vertical exchangecoefficients of mass,heat and momentum are computed with the introduction of subgridscale turbulenceenergy.The governing equations are solved by finite difference techniques.This model is applied to theJiaozhou bay to predict thermal pollution by the Huangdao power plant.An instantaneous tidal currentfield is computed,then the distribution of temperature increment is predicted,and finally the effect of windstress on thermal discharge is discussed.     

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.     

A three-dimensional hydrodynamic and salinity transport model of estuarine circulation with an application to a macrotidal estuary

A three-dimensional semi-implicit finite volume numerical model has been developed and applied to study tidal circulation and salinity stratification in the region of Oujiang River Estuary, China. The model employs horizontally unstructured grids and boundary-fitted coordinate system in the vertical direction. Governing equations consisting of continuity, momentum, and transport equations are all solved in the integral form of the equations, which provides a better representation of the conservative laws for mass, momentum, and transport in the coastal region with complex geometry and bottom bathymetry. The model performance was firstly quantified with skill assessment statistics on the choice of different parameters and validated with observed tidal elevation, current velocity, direction and salinity data over a spring–neap tidal cycle collected in 2006. Numerical results show that the model with wetting–drying capability successfully simulated the tidal currents and salinity fields with a reasonable accuracy and indicate that the Oujiang River Estuary is a macrotidal estuary with strong tidal mixing. In addition, the model results also show that the Oujiang River Estuary is a well-mixed estuary during spring tide. Then, the numerical simulations were performed to compare the hydrodynamic process and salinity distribution before and after a river training, which was conducted by blocking the south branch of the Oujiang River mouth. The results reveal that with the only north access to the sea, the influence of the blocking project on the flood discharge capacity is limited and the incremental velocity is beneficial to the navigation channel maintenance, although it will cause some scour to the embankment. Furthermore, the redistribution of tidal prism passing in or out the north branch makes a little severe salinity intrusion during high tide or low tide. However, the salinity intrusion is still within acceptable range, although it can cause some adverse effect on water intaking of production and life. The variations of salinity levels in Yueqing Bay situated at the north of the river mouth are not obvious, so the blocking project will not bring damage to local aquiculture. However, significant changes of salinity happen inside or outside of the south branch, so enough attention need to be paid to the changes of environment caused by the salinity variation after the blocking project. Overall, by weighing advantages and disadvantages of the blocking project, it is feasible and the model can be considered as a tool for managing and studying estuarine circulation.     

Least Square Finite Element Method for Viscous Splitting of Unsteady Incompressible Navier–Stokes Equations

In order to solve unsteady incompressible Navier–Stokes(N–S) equations, a new stabilized finite element method,called the viscous-splitting least square FEM, is proposed. In the model, the N–S equations are split into diffusive and convective parts in each time step. The diffusive part is discretized by the backward difference method in time and discretized by the standard Galerkin method in space. The convective part is a first-order nonlinear equation.After the linearization of the nonlinear part by Newton's method, the convective part is also discretized by the backward difference method in time and discretized by least square scheme in space. C~0-type element can be used for interpolation of the velocity and pressure in the present model. Driven cavity flow and flow past a circular cylinder are conducted to validate the present model. Numerical results agree with previous numerical results, and the model has high accuracy and can be used to simulate problems with complex geometry.     

Propagation and run-up of nearshore tsunamis with HLLC approximate Riemann solver

A numerical model describing the propagation and run-up process of nearshore tsunamis in the vicinity of shorelines is developed based on an approximate Riemann solver. The governing equations of the model are the nonlinear shallow-water equations. The governing equations are discretized explicitly by using a finite volume method. The nonlinear terms in the momentum equations are solved with the Harten-Lax-van Leer-Contact (HLLC) approximate Riemann solver. The developed model is first applied to prediction of water motions in a parabolic basin, and propagation and subsequent run-up process of nearshore tsunamis around a circular island. Computed results are then compared with available analytical solutions and laboratory measurements. Very reasonable agreements are observed.     

浮山湾帆船赛场水动力条件数值模拟

潮流数值计算是研究海域现状潮流场及预测潮流场分布的一个重要方法.根据帆船比赛的要求,结合青岛浮山湾及邻近海域的地理信息,应用分步杂交方法建立浮山湾变边界潮流数值模型进行模拟计算,分析浮山湾帆船赛场的水动力条件,从潮波、海水流速等方面证明选址的合理性.结果表明,浮山湾及附近海域的水动力和气候务件等均能够满足帆船比赛的要求.     

Internal inlet for wave generation and absorption treatment

A new method of implementing, in two-dimensional (2-D) Navier–Stokes equations, a numerical internal wave generation in the finite volume formulation is developed. To our knowledge, the originality of this model is on the specification of an internal inlet velocity defined as a source line for the generation of linear and non-linear waves. The use of a single cell to represent the source line and its transformation to an internal boundary condition proved to be an interesting alternative to the common procedure of adding a mass source term to the continuity equation within a multi-cell rectangular region. Given the reduction of the source domain to a one-dimensional region, this simple new type of source introduced less perturbation than the 2-D source type. This model was successfully implemented in the PHOENICS code (Parabolic Hyperbolic Or Elliptic Numerical Integration Code Series). In addition, the volume of fluid (VOF) fraction was used to describe the free surface displacements. A friction force term was added to the momentum transport equation in the vertical direction, in order to enhance wave damping, within relatively limited number of cells representing the sponge layers at the open boundaries. For monochromatic wave, propagating on constant water depth, numerical and analytical results showed good agreements for free surface profiles and vertical distribution of velocity components. For solitary wave simulation, the wave shape and velocity were preserved; while, small discrepancy in the tailing edge of the free surface profiles was observed. The suitability of this new numerical wave generation model for a two source lines extension was investigated and proven to be innovative. The comparisons between numerical, analytical and experimental results showed that the height of the merging waves was correctly reproduced and that the reflected waves do not interact with the source lines.     

A Hybrid Finite-Volume and Finite Difference Scheme for Depth-Integrated Non-Hydrostatic Model

A depth-integrated, non-hydrostatic model with hybrid finite difference and finite volume numerical algorithm is proposed in this paper. By utilizing a fraction step method, the governing equations are decomposed into hydrostatic and non-hydrostatic parts. The first part is solved by using the finite volume conservative discretization method, whilst the latter is considered by solving discretized Poisson-type equations with the finite difference method. The second-order accuracy, both in time and space, of the finite volume scheme is achieved by using an explicit predictor-correction step and linear construction of variable state in cells. The fluxes across the cell faces are computed in a Godunov-based manner by using MUSTA scheme. Slope and flux limiting technique is used to equip the algorithm with total variation dimensioning property for shock capturing purpose. Wave breaking is treated as a shock by switching off the non-hydrostatic pressure in the steep wave front locally. The model deals with moving wet/dry front in a simple way. Numerical experiments are conducted to verify the proposed model.     

近壁圆柱绕流水动力特性数值模拟与实验研究

通过数值模拟和物理模型实验,对距壁面一定高度的圆柱绕流水动力特性进行了研究。数值模拟采用有限体积法对标准k-ε模式方程进行离散,采用SIMPLE算法进行求解,模拟绕流流场。在物理模型实验中,将PVC圆管制作的实验模型安放在水槽内,在圆管的跨中沿表面周向均匀布置水下压力传感器,用于测量绕流圆柱体表面动水压力分布。通过改变Re数和间隙比来分析它们对近壁圆柱绕流水动力特性的影响。基于数值流动显示技术,给出了近壁绕流流场的尾流流态分析。通过数值结果与实验结果的对比,对近壁绕流圆柱体的升力系数及其表面动水压力分布进行了研究,对比结果显示了较好的一致性。