Numerical solution of the Saint-Venant equations by an efficient hybrid finite-volume/finite-difference method

A computationally efficient hybrid finite-volume/finite-difference method is proposed for the numerical solution of SaintVenant equations in one-dimensional open channel flows. The method adopts a mass-conservative finite volume discretization for the continuity equation and a semi-implicit finite difference discretization for the dynamic-wave momentum equation. The spatial discretization of the convective flux term in the momentum equation employs an upwind scheme and the water-surface gradient term is discretized using three different schemes. The performance of the numerical method is investigated in terms of efficiency and accuracy using various examples, including steady flow over a bump, dam-break flow over wet and dry downstream channels, wetting and drying in a parabolic bowl, and dam-break floods in laboratory physical models. Numerical solutions from the hybrid method are compared with solutions from a finite volume method along with analytic solutions or experimental measurements. Comparisons demonstrates that the hybrid method is efficient, accurate, and robust in modeling various flow scenarios, including subcritical, supercritical, and transcritical flows. In this method, the QUICK scheme for the surface slope discretization is more accurate and less diffusive than the center difference and the weighted average schemes.     

滑坡涌浪垂面二维数值模拟

 根据可压缩流连续方程和Navier-Stokes方程，推导出滑坡涌浪的控制方程，并建立了垂面二维滑坡涌浪数学模型。采用非规则贴体网格有限体积法和显示MacCormack法步进求解方程，并且利用新滩滑坡的相关资料进行了验证。结果表明，模型的计算值与原型观测值吻合较好。     

百色水电站尾水隧洞明满交替流动计算研究

百色水电站运行时,尾水隧洞中有可能出现明满交替流动而使尾水系统对电站运行的稳定性和过渡过程都带来复杂的影响,因此建立合理可行的明满交替流动数值模型是完全必要的。针对现有明满交替流动的数值解法中存在稳定性差的缺点,提出了一种新的计算方法——特征隐式格式法,其主要思路是将动量方程和连续方程转化为双曲型方程组的标准形式进行差分,并通过尾水隧洞水工水力学模型试验专门对该方法进行验证,表明该计算方法是正确的。将谊方法应用于百色水电站的尾水系统动态仿真计算中,并对尾水隧洞洞型进行优化,得到了满意的结果。     

THE MACCORMACK SCHEME AND THE BOUNDARY-FITTED COORDINATE SYSTEM FOR NUMERICAL SIMULATION OF SUPER CRITICAL FREE SURFACE FLOWS

1. INTRODUCTIONOpen channels carrying supercritical flows are commonly used in hydraulic engineering. Man-made structures such as spillway chutes, conveyance channels, sewer systems, and outlet works are some typical examples. Similarly, supercritical flo…     

NUMERICAL SOLUTION OF 2D FLOW USING A LOCAL COORDINATE SYSTEM

１．　ＩＮＴＲＯＤＵＣＴＩＯＮＴｈｅｒｅａｒｅｍａｎｙｅｆｆｅｃｔｉｖｅｍｅｔｈｏｄｓｉｎｎｕｍｅｒｉｃａｌｓｏｌｕｔｉｏｎｏｆｕｎｓｔｅａｄｙｔｗｏｄｉｍｅｎｓｉｏｎａｌｆｌｏｗ，ｓｕｃｈａｓｆｉｎｉｔｅｄｉｆｆｅｒｅｎｃｅｍｅｔｈｏｄ（ＦＤＭ），ｆｉｎｉｔｅｅｌｅｍｅｎｔｍｅｔｈｏｄ（ＦＥＭ），ｂｏｕｎｄａｒｙｅｌｅｍｅｎｔｍｅｔｈｏｄ（ＢＥＭ）ａｎｄｆｉｎｉｔｅａｎａｌｙｔｉｃｍｅｔｈｏｄ（ＦＡＭ）．ＴｈｅＦＤＭｈａｓｂｅｅｎｗｉｄｅｌｙｕｓｅｄｉｎｃｏｍｐｕｔａｔｉｏｎａｌｆｌｕｉｄ…     

THE SLOP FLUX METHOD FOR NUMERICAL BALANCE IN USING ROE＇S APPROXIMATE RIEMANN SOLVER

Imbalance arises when the Roe’s method is directly applied in the shallow water simulation.The reasons are different for the continuity equation and the momentum equations.Based on the Roe’s method,a partial surface method is proposed for a perfect balance for the continuity equation.In order to generate a mathematically hyperbolic formulation,the momentum equations are split,which causes incompatibility in the calculation of the momentum equations.In this article a numerical approach named the Slop Flux Method(SFM)is proposed to balance the source terms and the flux gradient based on the finite volume method.The method is first applied to shallow water equations.The model is verified by analytical results of classical test cases with good agreement.Finally the method is applied to a steady flow simulation over a practical complicated topography and the result shows good balance and conservation.     

基于变量分离的修正有限元数值计算

采用有限元方法直接求解粘性不可压缩流动N—S耦合方程，本文从离散化的动量方程和连续方程出发，得到了替代连续方程的压力简化统一方程，将各个求解变量分离开来，建立起直接从方程中求解压力场的有限元数值计算方法，有效地消除了压力场的伪震荡。通过对层流和紊流典型算例的分析比较，证明了本文方法是令人满意的。     

VOF方法模拟水面振荡流场

应用VOF(Volume of Fluid)方法结合不可压缩流体的N-S方程和连续性方程对矩形水池中的水面振荡流场进行数值模拟.采用共轭剩余法结合差分法求解N-S方程和连续性方程,采用施主-受主法求解流体体积函数控制方程.计算得到一个振荡周期内典型时刻矩形水槽水面振荡流场分布情况并与理论分析结果进行比较.并将计算得到的...     

HYBRID FINITE ANALYTIC SOLUTION FOR THREE-DIMENSIONAL TIDAL FLOW WITH SIGMA COORDINATE SYSTEM

1.　INTRODUCTIONTounderstandthecirculationandpollutanttransportinestuarineandcoastalwaters,numericalmodelshavebeenextensivelydevelopedduringthelasttwodecades.Thetransportofsalinity,heat,sedimentandwaterqualityconstituentwasdescribedbyadvectionanddiffusioninnumericalsimulations.Toconsidertheverticalvariation,inmanythree-dimensionaltransportmodels(SwansonandSpaulding1985;BlumbergandMllor1987;andSheng1987)thewell-knownσ-transformation(Philips1957)wasemployedinthepresenceofirrgularbathymtr…     

黄河河口水沙运动的二维数学模型

本文针对黄河河口河道水沙潮波的特点，从水流连续方程、运动方程，泥沙运动方程出发，补充了潮流挟沙能力的计算公式，建立了黄河河道河口二维数学模型。以1982年实测资料，从潮位过程、流速大小和方向及海底冲淤变形等方面对数学模型进行了验证计算。在此基础上开展了典型水沙条件下黄河河口泥沙运动规律的模拟研究。其结果揭示了黄河河口清水沟所处海域的潮流潮汐特性和泥沙输移规律。这些成果与实测资料以及卫星遥感分析结果一致，进一步表明了模型的可靠性。     

Modified Saint-Venant equations for flow simulation in tidal rivers

Flow in tidal rivers periodically propagates upstream or downstream under tidal influence. Hydrodynamic models based on the Saint-Venant equations (the SVN model) are extensively used to model tidal rivers. A force-corrected term expressed as the combination of flow velocity and the change rate of the tidal level was developed to represent tidal effects in the SVN model. A momentum equation incorporating with the corrected term was derived based on Newton’s second law. By combing the modified momentum equation with the continuity equation, an improved SVN model for tidal rivers (the ISVN model) was constructed. The simulation of a tidal reach of the Qiantang River shows that the ISVN model performs better than the SVN model. It indicates that the corrected force derived for tidal effects is reasonable; the ISVN model provides an appropriate enhancement of the SVN model for flow simulation of tidal rivers.     

二维浅水域潮流数值模拟的ADI－QUICK格式

本文采用ＡＤＩ－ＱＵＩＣＫ有限差分格式，用单一正交网格系进行空间离散，对二维浅水流动方程和污染物对流－扩散问题进行数值模拟。方法具有高阶精度，不呈现数值振荡，不带有可感受的数值衰减，计算过程稳定，计算方法简便等优点。本文以大连湾海域为实例，计算了Ｍ２－分潮流动规律。基于ＡＤＩ－ＱＵＩＣＫ格式编制的ＦＯＲＴＲＡＮ程序对其它的浅水海域和河口的流动问题具有普遍的适应性。     

复式河道一维洪水演进数值模拟

针对复式河道的特点,建立复式河道一维非恒定流数学模型,采用四点线性隐格式离散圣维南方程组,在动量方程中通过对主槽宽度进行修正,很好地解决了漫滩瞬间流量波动问题。通过2006年汛期调水调沙期间的实测资料对黄河下游白鹤—孙口河段洪水演进过程进行验证,结果表明,计算的洪峰变化过程比较符合实测情况,洪水传播时间的计算值与实测值基本吻合。     

波浪传播的数值模拟与物理模拟耦合模型

此文对于二维波浪的传播建立了数值模拟与物理模拟的耦合模型。模型中,数值模拟采用基于改进Boussinesq方程的三角形网格有限元模型,物理模拟采用推板式造波机。模型的求解采用空间五点的拉格朗日插值和时间的四阶Runge-Kutta格式。通过波浪模拟实验研究了耦合模型在不同波浪要素下的适应性。进一步针对于规则波和不规则波分别建立了实时修正由于造波机造波性能所引起的模拟误差的方法。波浪模拟实验结果表明,耦合边界附近数模结果与物模结果吻合很好,实时修正方法能很好修正由于造波机造波性能所引起的模拟误差,耦合模型和实时修正方法能有效建立起数模与物模的确定性联合。     

丁坝对弯道水流水力特性影响的研究

针对丁坝对弯道水流水力特性影响的问题,建立了相应的概化模型,通过数值模拟的方法,利用RNG k-湍流模型封闭Reynods方程,VOF法追踪自由表面,通过有限体积法离散求解,模拟研究了不同弯道中心角情况下,丁坝对弯道水流横向水面超高和流速场的影响。结果表明:在丁坝影响下,弯道水流水面横比降计算公式需要进行修正,应当考虑丁坝对河道的束窄、丁坝尺寸和弯道角度等综合因素的影响。     

THREE-DIMENSIONAL SIMULATION OF MEANDERING RIVER BASED ON 3-D RNG k-ε TURBULENCE MODEL

A 3-D numerical model for calculating flow in non-curvilinear coordinates was established in this article. The flow was simulated by solving the full Reynolds-averaged Navier-Stokes equations with the RNG k-ε turbulence model. In the horizontal x-y-plane, a boundary-fitted curvilinear co-ordinate system was adopted, while in the vertical direction, a co-ordinate transformation was used to represent the free surface and bed topography. The water level was determined by solving the 2-D Poisson equation derived from 2-D depth averaged momentum equations. The finite-volume method was used to discretize the equations and the SIMPLEC algorithm was applied to acquire the coupling of velocity and pressure. This model was applied to simulate the meandering channels and natural rivers, and the water levels and the velocities for all sections were given. By contrasting and analyzing, the agreement with measurements is generally good. The feasibility studies of simulating flow of the natural river have been conducted to demonstrate its applicability to hydraulic engineering research.     

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.     

数值模拟波浪翻越直立方柱

本文应用ＶＯＦ方法研究了孤立波翻越直立方柱流动的全过程。用人工压缩法和差分法求解二维Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程，用施主－受主法求解流体体积函数控制方程。通过数值计算得到了孤立波翻越直立方柱的流场和压力值，并成功地模拟出波浪涌顶，水柱喷射，冲击和界面破碎的过程。     

绕圆柱非定常周期性涡旋脱落的数值模拟

利用非定常流函数涡量方程数值模拟圆柱突然起动尾流涡旋的形成及周期性脱落过程。对求解的流函数的一阶导数即速度项采用四阶精度的Hermitian公式，而方程的对流项则采用四阶精度的差分格式，并利用ADI方法迭代求解差分方程组。当雷诺数Re不大于40时，圆柱尾流为附体的两个对称涡，为定常解。当Re大于40后流动为非定常及非对称的，圆柱尾流呈现周期性涡旋交替脱落而形成著名的Karman涡街。选择Re=100为例，在初始条件未加任何扰动情况下，成功地模拟了圆柱非定常涡旋形成与脱落的完整过程（无量纲时间算到t=250及以上）。所计算的阻力系数与实验结果及其它数值方法的计算结果一致。约在t=200形成严格的Karman涡街。对涡量方程ADI求解方法的稳定性进行了分析。对流项采用四阶精度差分格式，若应用于定常问题，将极大提高数值求解的精度，若应用于非定常问题的求解，将对求解精度有所改善，其中时间空间两阶混合偏导数的处理是关键，有待进一步的数值实验。     

THREE-DIMENSIONAL NUMERICAL MODEL FOR WINDING TIDAL RIVER WITH BRANCHES

Natural rivers are usually winding with branches and shoals,which are difficult to be simulated with rectangular grids. A 3-D current numerical model was established based on the orthogonal curvilinear coordinate system and vertical σ coordinate system. The equations were discretisized using a semi-implicit scheme. The “predictor” and “corrector” steps were applied for the horizontal momentum equations to meet the basic requirement that the depth-integrated currents obtained from the equations for 2-D and 3-D modes have identical values. And a modification of traditional method of dry/wet discriminance was proposed to determine accurately the boundary and ensure the continuity of variable boundary in the simulation. This model was verified with the data measured in a winding tidal river with branches in April,2004. The simulated data of water levels and velocities agree well with the measured ones,and the computed results reveal well the practical flow characteristics,including the vertical secondary flow in a winding reach.