WATER WAVE SIMULATION IN CURVILINEAR COORDINATES USING A TIME-DEPENDENT MILD SLOPE EQUATION

The purpose of this article is to model the detailed progress of wave propagation in curvilinear coordinates with an effective time-dependent mild slope equation. This was achieved in the following approach, firstly deriving the numerical model of the equation, i.e., Copeland's hyperbolic mild-slope equation, in orthogonal curvilinear coordinates based on principal of coordinate transformation, and then finding the numerical solution of the transformed model by use of the Alternative Directions Implicit (ADI) method with a space-staggered grid. To test the curvilinear model, two cases of a channel with varying cross section and a semi-circular channel were studied with corresponding analytical solutions. The model was further investigated through a numerical simulation in Ponce de Leon Inlet, USA. Good agreement is reached and therefore, the use of the present model is valid to calculate the progress of wave propagation in areas with curved shorelines, nearshore breakwaters and other complicated geometries.     

一种适于复杂形状物体绕流计算的网格生成方法

本文给出了一种适用于复杂形状边界下进行复杂流动数值模拟的有效的网格生成方法，该方法将求解域分成若干个子域，由子域边界点分布来确定Ｐｏｉｓｓｏｎ方程源项，从而控制求解域内点分布，在全场求解Ｐｏｉｓｓｏｎ方程。所生成的网格质量高，且避免了用普通ＴＴＭ法生成网格时，网格疏密分布的控制过于依赖于经验参数的选择的缺点，作为例证，给出了环量控制翼型绕流的数值模拟结果。     

NUMERICAL SIMULATION OF 2-D TIDAL FLOW AND WATER QUALITY UNDER THE CURVILINEAR COORDINATES

This paper presents a numerical method to simulate the 2-D tidal flow and water quality under the curvilinear coordinates. In order to overcome the computational difficulties in natural rivers, such as the complicated boundary figures, the great disparity between length and width of computational domain, etc. , boundary-fitted grid is used, the irregular domain in physical plane is transformed into a rectangular domain in transformed plane, and the depth-averaged momentum equations and mass equation are rewritten and discretized based on the finite volume techniques in curvilinear coordinates. Practical application of the method is illustrated by an example for the Dachangzhen Section of the Yangtze River. A fair agreement between the values measured and computed demonstrates the validity of the method developed.     

船舶螺旋桨周围粘流场数值预报与流场分析

本文叙述了通过直接求解雷诺平均应力方程（ＲＡＮＳ）来获得船舶螺旋桨粘流场数值解的方法与数值求解步骤，该方法采用非交错网格系统，利用幂函数格式离散动量方程，预报－校正方法求解速度－压力耦合问题，应用Ｂａｌｄｗｉｎ－Ｌｏｍａｘ代数湍流模式求解雷诺应力项使方程组封闭，以此来获得螺旋桨粘流场，为了验证数值方法的稳定性和可靠性，文中以ＤＴＲＣ４１１９桨为算例，对螺旋桨粘流场进行了数值求解，通过对计算结果的分     

求解不可压层流的一种全隐数值格式

该文基于SMAC(simplified marker and cell)方法,发展了一种在任意曲线坐标系中求解不可压黏性层流的全隐数值格式。基本方程是以逆变速度为未知变量的动量方程和关于压力修正量的Poisson方程。所有方程离散在MAC交错网格系统中进行。根据构造的全隐数值格式自编程序对一可简化成二维层流的后台阶流场进行计算,通过与已有的实验结果和计算结果进行比较,确认目前的计算结果优于比较的计算结果,和实验结果也相当吻合。为进一步验证该数值格式的可靠性,扩展程序对三维后台阶层流进行计算,结果表明,三维计算结果比二维计算结果更加接近实验结果。     

长江口边界拟合坐标的三维潮流数学模型

在正交曲线坐标系下 ,采用坐标变换、有限差分、交替隐式求解、动边界处理等方法 ,建立了边界拟合网格的三维潮流数学模型 .应用在长江口潮流场的计算中 ,得到了与长江口实测潮位、流速和流向相一致的结果 ,能较好地反映长江口复杂边界和地形下的三维潮流场变化     

Tracer advection in an idealised river bend with groynes

This paper presents numerical simulations of particle advection in the bend of an open channel containing groynes, which is an idealised form of a shallow river bend in a wide river. The flow field is computed using a boundary-fitted solver of the non-orthogonal, curvilinear shallow water equations. The computational grid is generated by solving Poisson-type elliptic partial differential equations using an iterative multi-grid scheme for prescribed boundary coordinates. The shallow water equations are discretised with finite differences in space, and 4 t h order Runge-Kutta integration in time. Tracers introduced at specific initial locations have their trajectories computed using Lagrangian particle tracking. The numerical shallow flow model is verified by comparison to the analytical solution of fully developed flow in an open channel. The combined shallow flow and Lagrangian particle-tracking model is then used to simulate the advection of tracer particles in a rectangular channel containing a pair of parallel groynes, and tracer particles in a curved open channel containing groynes, of dimensions roughly equivalent to a Danube River bend.     

HIGH ACCURATE SOLUTION OF INCOMPRESSIBLE VISCOUS FLOW WITH PRIMATIVE VARIABLE

This paper presents a higher order difference scheme for the computationof the incompressible viscous flows.The discretization of the two-dimensional incompress-ible viscous Navier-Stokes equations,in generalized curvilinear coordinates and tensor for-mulation,is based on a non-ataggered grid.The momentum equations are integrated intime using the four-stage explicit Runge-Kutta algorithm [1]and discretized in space us-ing the fourth-order accurate compact scheme[2]The pressure-Poisson equation is dis-cretized using the nine-point compact scheme.In order to satisfy the continuity constraintand ensure the smoothness of pressure field,an optimum procedure to derive a discretepressure equation is proposed [9][3]The method is applied to calculate the driven cavityflow on a stretched grid with the Reynolds numbers from 100 to 10000.The numerical re-sults are in very good agreement with the results obtained by Ghia et al [7]and includethe periodic solutions for high Reynolds numbers.     

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。     

水生植物对河道形态影响的三维湍流模型

植被是河床和河岸稳定性指标中的一个重要参数,它主要通过影响水流结构进而影响河道的形态。本文建立曲线坐标系下的三维湍流模型研究水生植物对河道形态的影响,在水流控制方程中加入植物阻力项和植物密度项来描述水生植物对水动力特性的贡献,通过泥沙质量守恒方程求解河道变形,在适体网格中求解模型的控制方程。应用该三维模型数值模拟了矩形水槽内两侧交替布置的非淹没刚性植物对水流结构的影响以及梯形河道内两侧交替布置的非淹没刚性植物对河道形态的影响,数值计算结果与实测结果吻合良好。     

曲线坐标系下波浪传播的数学模型及其比较与验证

引入自适应网格技术，建立了曲线坐标系下考虑能耗影响的缓变水深水域波浪传播的数值模拟模型，通过在模型中引入能量耗散项以更好地处理全透射边界。基于原型缓坡方程，完善了等水深的轴对称双导堤水域内波浪传播的精确解表达式及其计算结果；提供了等水深的环形河道水域内较为详细的精确解。在极坐标系下就等水深的轴对称双导堤水域内波浪的传播，推导了缓坡方程的小角度抛物近似模型的解析解表达式。就上述两水域内波浪传播的数值模拟模型的数值解、抛物近似模型的解、精确解进行了详细比较，说明数值解与精确解相吻合、数值模拟模型比小角度和大角度抛物近似模型具有更高的精度。数值模拟模型能较好地模拟水深复杂变化的地形上波浪的传播，能有效反映波浪传播过程中的多种物理现象。     

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).     

田市抽水站进水前池水力特性数值模拟

借鉴有关弯道水流流速分布的研究成果,计入弯道环流引起的横向动量交换,对曲线坐标系平面二维浅水方程做了修正;采用边界处正交的曲线网格生成技术,处理复杂的计算区域边界。采用修正后的模型对田市抽水站进水前池改造前后的水流流态作模拟分析,来验证改造设计方案的合理性。     

DISTRIBUTION OF WAVE-INDUCED EXCESS MOMENTUM FLUXES OVER DEPTH AND APPLICATION TO THREE-DIMENSIONAL NUMERICAL MODELING OF WAVE-CURRENT INTERACTIONS

1.　ＩＮＴＲＯＤＵＣＴＩＯＮＩｎｔｈｅｓｔｕｄｙｏｆｗａｖｅｄｙｎａｍｉｃｓ,ＬｏｎｇｕｅｔＨｉｇｇｉｎｓａｎｄＳｔｅｗａｒｔｈａｖｅｐｒｅｓｅｎｔｅｄｔｈｅｗａｖｅｉｎｄｕｃｅｄｅｘｃｅｓｓｍｏｍｅｎｔｕｍｆｌｕｘｅｓｉｎｔｉｍｅａｖｅｒａｇｅｄａ?..     

二维同位与交错网格水流数值模拟比较

在边界拟合正交曲线坐标系下,建立了求解变量分别位于同位与交错网格条件下的二维水流数值模拟计算模式。利用实验资料对其进行了验证,同时对两种模式的计算结果进行了比较分析。在运用界面动量插值的条件下,采用同位网格模式对二维流场进行数值模拟可获得较满意的结果。     

弯道水流的两步隐式算法研究

采用优于SIMPLEC算法的两步隐式解法求解二维曲线坐标系下的浅水方程,建立了二维弯道水流数学模型。对流项采用二阶精度的Roe格式离散;物理变量采用适体坐标系下的同位网格布置,网格界面流速由动量插值法计算;紊动黏性系数由修正的k-ε模型确定。采用此模型对弯道内的水流流动进行了数值模拟,计算结果和实测数据吻合较好。     

曲线坐标网格下二维涌波数值模拟的TVD型格式

针对水动力学中的涌波现象导出二维曲线坐标系下的守恒型方程，然后利用算子分裂法和TVD差分格式思想构造出计算格式，在此基础上建立起由实际流场区域至方形计算区域的全局同胚映射，对急流过缩窄河道产生的涌波结构进行数值模拟，结果表明，本文的数值方法能够很好地模拟附体涌波、交叉涌波等复杂结构现象，所得波系结构和有关物理量与理论分析结果非常吻合，表明本文的数值方法对于模拟水动力学中的涌波现象是可行的。     

NUMERICAL SOLUTION FOR TURBULENT FLOWS ON CONCAVE SURFACES OF SPILLWAY DAMS

1.INTRODUCTIONInthenumericalsolutionofturbulentflows,numerousturbulencemodelshavedemonstratedavarietyofgoodnumericalpredictionsbothqualitativelyandquantitatively.Amongthem,thek--smodelisthemostwidelyemployedisotropictwo--equationmodel.Ithasbeenextensivelyappliedtodifferentturbulentflowproblems.However,thestandardk--Emodelappearstobeinsufficientinpredictingthecomplexturblentshearlayers,suchasflowssubjectedtocurvatureandrotation.Thesensitivityofturbulentflowcharacteristicstoevensmallamount…     

NUMERICAL STUDY OF SOLITARY WAVE FISSION OVER AN UNDERWATER STEP

Solitary wave fission over an underwater step is numerically investigated. The numerical model is based on the enhanced Boussinesq equations, which appropriately represent both the nonlinearity and dispersivity of surface water waves. The finite difference method defined on the staggered grid in space with an implicit scheme for time stepping is employed for the numerical solution of the governing equations. It is demonstrated that Boussinesq type equations, though they are vertically integrated, can describe the details of the solitary wave fission process with very good accuracy. Numerical results of the reflected and transmitting wave heights, the number of solitons emitted from the transmitting wave and their amplitudes all agree very well with the analytical solution derived from KdV equation by virtue of a linear long wave approximation in the vicinity of the underwater step.     

闸下有压渗流的边界拟合坐标变换数值解

建立了曲线拟合坐标系下闸下渗流的数学模型 ,给出了边界条件和求解方程。计算实例表明 ,该数学模型对水利工程中的复杂边界渗流的数值求解很有效 ,可应用于工程实际