三维定常船尾绕流的不定常数值计算

本文采用有限体积法非正交贴体会标下对求解三维不定常船尾绕流做了进一步的研究，将Ｃａｒｒｔｅｅｉａｎ坐标系下的Ｎ－Ｓ方程和连续方程变换到非正交贴坐标系下的方程，用ＳＩＭＰＬＥＣ方法迭代求解速度和压力耦合的有限差分方程组，最后给出了用该方法计算的ＳＳＰＡ７２０例子。     

2-D FLOW AND SEDIMENT SIMULATION FOR THE FLOOD REGULATION OF A RESERVOIR WITH WATER INTAKE

In this paper, the flood regulation by operating the downstream sluice gates for a reservoir with a water intake is studied. The two-dimensional depth-averaged flow equations are solved by the boundary fitted finite volume method (FVM) based on MacCormsck prediction-correction scheme. The bed deformation caused by both the bed load and incoming suspended sediment is determined in a coupled way. The model is used to simulate the practical flood regulation operation of a reservoir. The results have been compared with the physical experiment.     

SIMULATION OF SEDIMENT-LADEN FLOW BY DEPTH-AVERAGED MODEL BASED ON UNSTRUCTURED COLLOCATED GRID

The 2-D depth-averaged mathematical model for sediment-laden flows has been widely used in river control and other related engineering problems, and now it is usually solved on structured grids. Since the natural river is usually very complicated in plane boundary, and unstructured grids are more attractive in solving the problems with complicated domains, the following questions about solving 2-D depth-averaged model were discussed in this article: (1) a modified Bowyer algorithm was suggested to generate unstructured grids for natural rivers, (2) the Finite Volume Method (FVM) is employed to discretize the governing equations of the 2-D depth-averaged model and an implicit scheme was suggested with unstructured collocated grids, (3) the observed hydrological data of the Chenglingji Reach in the Yangtze River are used for verification of the presented method. It seems that the suggested numerical scheme works very well, and the simulation results of both hydraulic characteristics and river bed deformation are in good agreement with the observed ones.     

非正交网格有限体积法在三维潮流场计算中的应用

有限体积法是求解流体问题的一个非常有效的数值方法，本文研究非正交网络有限体积法在三维潮流场数值模拟中的应用。由三维浅水方程出发，利用有限体积法的积分模式并引入Ｇｒｅｅｎ－Ｇａｕｓｓ公式，将控制体单元的体积分转化为面积分，采用一种任意六面体单元，垂直涡动粘性系数定义为水深的函数，使之能适应复杂海哉和地形，又可获得不同水深的计算数据。     

APPLICATION OF FDS SCHEME TO 2D DEPTH-AVERAGED FLOW-POLLUTANTS SIMULATION

1 .　INTRODUCTIONSincethe 1990’s ,severalhigh resolutionschemesadoptedintheaerodynamicsfieldhavebeenappliedtodepth averagedtwo dimensional(2D)flowsimulation (Tan 1992 ,Alcrudo 1993andZhaoetal .1994a ,1996 ) .Someofthem ,suchastheOsherandFluxVectorSplitting (FVS )schemes,havebeenimprovedtoestimatethenu mericalfluxacrosstheinterfacebetweencellsinthe 2Dcoupledflow pollutantmodel (Qietal.1998andZhaoetal.1994b ,2 0 0 0 ,2 0 0 2 ) .Thehigh resolutioncharacteristic basedupwindFulxDifferen…     

NUMERICAL SIMULATION FOR 2D SHALLOW WATER EQUATIONS BY USING GODUNOV-TYPE SCHEME WITH UNSTRUCTURED MESH

1. INTRODUCTION In general, the geometry of natural water areas, such as rivers, coasts and lakes, is irregular, so that the application of mathematical models with structured mesh is quite limited and the accuracy could not be ensured especially as the m…     

悬浮物输运的数学模型

为了研究镇江内湖悬浮物的输移运动规律，建立了二维悬浮物输运数学模型。模型考虑了风场及潮流作用下悬浮物的输运，同时还考虑了悬浮物的沉降和再悬浮机制，采用切应力概念确定悬浮物的起悬量和沉降量。在无结构网格上对水流和悬浮物输运方程进行有限体积的积分离散，应用高性能的Osher格式计算水量、动量及悬浮物输运等通量，提高了数值模拟的精度。应用2次大规模水文和悬浮物含量的野外同步监测资料对模型进行了验证。模拟值与实测值吻合较好，表明模型能合理地反映内湖水流及悬浮物的运动规律。     

西江金利镇段的水流-水质数值模拟研究

建立了基于有限体积法的二维水流水质数学模型体系,并采用水位床底方程法（ Water Level bottom topography Formulation, WLF）处理底坡源项,保证计算格式的和谐性。将模型运用到西江金利镇段水流水质数值模拟中,模拟得到西江金利段水动力情况与实测值吻合度高,同时预测得到的污染物浓度较合理。模拟结果表明,有必要对金利镇生活污水及生产废水采取措施,加强区域环境管理,以保障该河段水质安全。     

EFFECT OF ESCAPE DEVICE FOR SUBMERGED FLOATING TUNNEL （SFT） ON HYDRODYNAMIC LOADS APPLIED TO SFT

This paper presents a potential approach to settle the problem of surviving major safety accidents in Submerged Floating Tunnel (SFT) that detachable emergency escape devices are set up outside SFT. The Computational Fluid Dynamics (CFD) technology is used to investigate the effect of emergency escape devices on the hydrodynamic load acting on SFT in uniform and oscillatory flows and water waves by numerical test. The governing equations, i.e., the Reynolds-Averaged Navier-Stokes (RANS) equations and standard turbulence equations, are solved by the Finite Volume Method (FVM). Analytic solutions for the Airy wave are applied to set boundary conditions to generate water wave. The VOF method is used to trace the free surface. In uniform flow, hydrodynamic loads, applied to SFT with emergency escape device, reduce obviously. But, in oscillatory flow, it has little influence on hydrodynamic loads acting on SFT. Horizontal and vertical wave loads of SFT magnify to some extend due to emergency escape devices so that the influence of emergency escape devices on hydrodynamic loads of SFT should be taken into consideration when designed.     

模拟水质突跃问题的三种二阶高性能格式

在有限体积法和黎曼近似解理论框架下建立三种二阶TVD格式(Total Variation Diminishing Scheme全变差消减格式)。通过理想条件下方形浓度场在均匀流场中的输移这一算例，分析了在水质间断情况下三种格式的计算精度。与一阶逆风格式的计算结果进行了比较，结果表明，所建的三种二阶TVDS格式的计算精度显著高于一阶逆风格式，与理论值吻合较好，说明所建三种格式适用于水质突跃(包括水质间断)情况的水质预测。     

A second-order Finite Volume Method for pipe flow with water column separation

A second-order explicit Finite Volume Method (FVM) based on Godunov-type schemes is presented and applied to water column separation (WCS) in pipelines. The treatment of two-phase fluid in the model is similar to the ideas of the classic discrete vapor cavity model (DVCM) based on method of characteristics (MOC). The challenge in using the FVM is how to capture vapor cavities and predict their growth and collapse. The FVM introduced here assumes the vaporous cavity is concentrated at the middle of control volume, and divides the local control volume into two equal halves, in order to calculate the vapor cavity volume. The proposed model is based on the exact Reimann solution of the coupled continuity and momentum equations, and second-order accuracy is achieved by means of data reconstruction based on slope limiter, an approach which prevents the development of spurious oscillations near in the vicinity of high gradients. Predictions of FVM-DVCM for transient pressures caused by WCS and rejoining are compared to published experimental data and to numerical results from the classic DVCM. Pressure results from FVM-DVCM show considerably better agreement with experimental data and significantly avoid unrealistic artificial spikiness with finer grids.     

长江江苏段二维水流-水质模拟

根据长江江苏感潮河段水流水质及地形特点，应用有限体积法及黎曼近似解建立了平面二维水流-水质模型。模型应用有限体积法的积分离散，并利用通量坐标旋转的不变性把二维问题转化为一系列局部的一维问题进行求解，采用通量差分裂格式计算各跨单元边界的水量、动量及污染物输运等通量。应用浓度输移精确解验证模型算法的正确性，利用长江江苏感潮河段的水流、水质监测资料进行模型率定检验，并通过对卫星遥感资料的分析检验模型计算污染带的合理性。模型在长江江苏段主要地区区域供水规划及实施决策支持系统中得到应用，为该江段水质规划提供依据。     

Multi-scale Runge-Kutta_Galerkin method for solving one-dimensional KdV and Burgers equations

In this paper, the multi-scale Runge-Kutta_Galerkin method is developed for solving the evolution equations, with the spatial variables of the equations being discretized by the multi-scale Galerkin method based on the multi-scale orthogonal bases in 0(,)mH a b and then the classical fourth order explicit Runge-Kutta method being applied to solve the resulting initial problem of the ordinary differential equations for the coefficients of the approximate solution. The proposed numerical scheme is validated by applications to the Burgers equation(nonlinear convection-diffusion problem), the Kd V equation(single solitary and 2-solitary wave problems) and the Kd V-Burgers equation, where analytical solutions are available for estimating the errors. Numerical results show that using the algorithm we can solve these equations stably without the need for extra stabilization processes and obtain accurate solutions that agree very well with the corresponding exact solutions in all cases.     

Numerical simulation of the internal wave propagation in continuously densitystratified ocean

A numerical model is proposed to simulate the internal wave propagation in a continuously density-stratified ocean, and in the model, the momentum equations are derived from the Euler equations on the basis of the Boussinesq approximation. The governing equations, including the continuity equation and the momentum equations, are discretized with the finite volume method. The advection terms are treated with the total variation diminishing （TVD） scheme, and the SIMPLE algorithm is employed to solve the discretized governing equations. After the modeling test, the suitable TVD scheme is selected. The SIMPLE algorithm is modified to simplify the calculation process, and it is easily made to adapt to the TVD scheme. The Sommerfeld＇s radiation condition combined with a sponge layer is adopted at the outflow boundary. In the water flume with a constant water depth, the numerical results are compared to the analytical solutions with a good agreement. The numerical simulations are carried out for a wave flume with a submerged dike, and the model results are analyzed in detail. The results show that the present numerical model can effectively simulate the propagation of the internal wave.     

A NEW FINITE DIFFERENCE SCHEME FOR 2-D FLOWS AT LARGE Re

Based on the conventional ADI method and SOR method for solving the Navier-Stokes equations, averaging those linkage terms which also are the terms of vary-ing coefficients of the equations, a new finite difference scheme-Averaging Finite Diffe-rence (AFD) scheme for 2-D flows was proposed. A 2-D driven cavity flow was calculated numerically as an example with the presented scheme at Re= 100, 1000, 2000, 3200, 10000. The results were discussed and compared to those obtained with the conventional methods as well as experimental data. It showed that a slight change of the approximation pattern of the conventional scheme in the terms of varying-coefficients of the governing equations seems to have an obvious influence on the solutions at high Re which will be erro- neous if the conventional schemes was employed.     

对流扩散反应型方程的一种稳定的算子分裂格式

首先提出了一种求解三维对流扩散反应型方程的算子分裂格式:DF-AD-REA分裂格式。处理纯对流算子时,采用特征线法,而扩散算子和反应项则采用显式差分格式。证明了:当Δt≤Min时,整个分裂算法是稳定的。这里,v是扩散系数的最大值,Nd是空间维数,h和U分别为i方向的空间步长和速度分量,Δt是时间步长。然后,选择一些线性和非线性的对流扩散反应型方程,用数值解与相应分析解的比较来检验算法的收敛性与精度,结果表明算法是有效的。由于算法简单、稳定,且对一、二维空间问题均适用,故可用于粘性流体流动、传质过程(如大气或河流等环境中污染物的传输)以及传热过程(如热、核电厂中的冷却水问题)等众多实际问题的计算中。     

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.     

NONSTRUCTED GRID MESH FINITE VOLUME METHOD AND APPLICATION

Finite Volume Method (FVM) which can solve fluid problems effectively is used in this paper. Gauss theorem is used to transfer volume integration to area integration , by which the relation formula of the nodes around each element is founded based on the constancy of the flux into and out of the element. With that the discrete equations are obtained. This method with free cubic element is applied in 3D seepage and tidal flow problems. From the practice it can be found that seepage flux is more accurate than FEM and FVM also has the advantages of good stability, convenience of solving. easy programming, less computing time and storage.     

NUMERICAL INVESTIGATION ON EXTRUDATE SWELL FOR VISCOELASTIC FLUID： USING MAXWELL MODEL

The numerical investigation on extrudate swell through capillary die for viscoelastic fluid characteried by integral-type Maxwell constitutive equation was conducted by employing the finite element method with the calculation of viscoelastic extra stress in the conventional finite element. The method of avoiding singularity was also adopted by integrating the strain history of the Gauss points for each element near the wall and the free surface. The convergence solutions at high Weissenberg number can be obtained by using the appropriate methods to reduce errors and improve the speed of convergence of the calculation, which include adding a relaxation factor of velocity in iteration process, or enlarging the reference viscosity, or reducing the elapsed time. The highest Weissenberg number obtained here is up to 3. 8, while the solution at the Weissenberg number of 3. 75 was given in the previous work with similar extrudate swell ratio and the exit pressure drop by using differential Maxwell model with Elastic-Viscous Stress Split (EVSS) combined with Streamline Upwind Petrov-Galerkin (SUPG) scheme. The calculations indicated that the method of dealing with integral consti- tutive equation introduced in this paper is suitable in simulating viscoelastic flow characterized by integral constitutive equation at high elastic level.     

A CHARACTERISTIC-BASED FINITE VOLUME SCHEME FOR SHALLOW WATER EQUATIONS

We propose a new characteristic-based finite volume scheme combined with the method of Central Weighted Essentially Non-Oscillatory (CWENO) reconstruction and characteristics, to solve shallow water equations. We apply the scheme to simulate dam-break problems. A number of challenging test cases are considered, such as large depth differences even wet/dry bed. The numerical solutions well agree with the analytical solutions. The results demonstrate the desired accuracy, high-resolution and robustness of the presented scheme.