MODELING DAM-BREAK FLOOD OVER NATURAL RIVERS USING DISCONTINUOUS GALERKIN METHOD

A well-balanced numerical model is presented for two-dimensional, depth-averaged, shallow water flows based on the Discontinuous Galerkin (DG) method. The model is applied to simulate dam-break flood in natural rivers with wet/dry bed and complex topography. To eliminate numerical imbalance, the pressure force and bed slope terms are combined in the shallow water flow equations. For partially wet/dry elements, a treatment of the source term that preserves the well-balanced property is presented. A treatment for modeling flow over initially dry bed is presented. Numerical results show that the time step used is related to the dry bed criterion. The intercell numerical flux in the DG method is computed by the Harten-Lax-van Contact (HLLC) approximate Riemann solver. A two-dimensional slope limiting procedure is employed to prevent spurious oscillation. The robustness and accuracy of the model are demonstrated through several test cases, including dam-break flow in a channel with three bumps, laboratory dam-break tests over a triangular bump and an L-shape bend, dam-break flood in the Paute River, and the Malpasset dam-break case. Numerical results show that the model is robust and accurate to simulate dam-break flood over natural rivers with complex geometry and wet/dry beds.     

溃坝水流在复杂河道中传播的三维数值模拟

为研究河道弯曲和障碍物对溃坝波传播的影响,采用有限体积法对描述水流运动紊流模型和描述自由水面运动的VOF方程进行离散,建立了溃坝水流运动的三维数学模型,并对急弯河道进行了数值模拟计算。急弯河道溃坝波传播过程的模拟结果与前人实体模型试验结果基本一致。利用该模型研究了丁坝附近溃坝波传播的特性和溃坝水流的内部结构,数值模拟结果表明,溃坝波的传播受河道弯曲或障碍物的影响,产生反射和绕射,使得局部溃坝水流呈明显的三维特性。上游丁坝迎水面受到溃坝波波前的直接冲击,其动水压力远大于作用于下游丁坝的动水压力。另外,障碍物对溃坝水流的影响主要局限在障碍物上游和下游一定范围内,在此范围外,水流呈二维或一维特性。     

基于GIS与支持向量机的溃坝损失评估

 针对溃坝损失评估涉及众多地理空间对象且影响因素多而复杂的特点,提出了GIS支持下基于支持向量机的溃坝损失评估方法。分析了溃坝损失的计算方法及其影响因素,通过灰色关联度模型建立了评估指标体系。详细探讨了GIS与支持向量机模型相结合进行溃坝损失评估的方法与实现过程。应用表明,该评估方法精度较高,效果较好。     

Study of total variation diminishing (TVD) slope limiters in dam-break flow simulation

A two-dimensional (2D) dam-break flow numerical model was developed based on the finite-volume total variation diminishing (TVD) and monotone upstream-centered scheme for conservation laws (MUSCL)-Hancock scheme, which has second-order accuracy in both time and space. A Harten-Lax-van Leer-contact (HLLC) approximate Riemann solver was used to evaluate fluxes. The TVD MUSCL-Hancock numerical scheme utilizes slope limiters, such as the minmod, double minmod, superbee, van Albada, and van Leer limiters, to prevent spurious oscillations and maintain monotonicity near discontinuities. A comparative study of the impact of various slope limiters on the accuracy of the numerical flow model was conducted with several dam-break examples including wet and dry bed cases. The numerical results of the superbee and double minmod limiters agree better with the theoretical solution and have higher accuracy than other limiters in one-dimensional (1D) space. The ratio of the downstream water depth to the upstream water depth was used to select the proper slope limiter. For the 2D numerical model, the superbee limiter should not be used, owing to significant numerical dispersion.     

AN UNSTRUCTURED FINITE-VOLUME ALGORITHM FOR NONLINEAR TWO-DIMENSIOAL SHALLOW WATER EQUATION

An unstructured finite-volume numerical algorithm was presented for solution of the two-dimensional shallow water equations, based on triangular or arbitrary quadrilateral meshes. The Roe type approximate Riemann solver was used to the system. A second-order TVD scheme with the van Leer limiter was used in the space discretization and a two-step Runge-Kutta approach was used in the time discretization. An upwind, as opposed to a pointwise, treatment of the slope source terms was adopted and the semi-implicit treatment was used for the friction source terms. Verification for two-dimension dam-break problems are carried out by comparing the present results with others and very good agreement is shown.     

基于二维溃坝波数值模拟的生命损失估算

通过界面数值通量以及底坡源项的计算求解无碰撞二维Boltzmann方程,建立了二维溃坝波数值模型.以杭州市余杭镇上游某水库为例,模拟了该水库溃坝后溃坝波的演进过程,模拟结果表明溃坝洪水淹没范围很大,距坝约11 km的下游,水深仍可达4.0 m以上.同时,应用通用的溃坝生命损失模型,在获取网格单元上的水力学参数值（包括水深和最大流速）基础上,输入当地的地形、人口等基本数据,估算了水库溃坝对下游造成的生命损失.该方法可用于其他水库的风险管理分析,为相关部门决策提供依据和参考.     

Numerical simulation of flow and bed morphology in the case of dam break floods with vegetation effect

The purpose of this study is to establish a depth-averaged 2-D hydrodynamic and sediment transport model for the dambreak flows with vegetation effect. The generalized shallow water equations are solved using an explicit finite volume method with unstructured quadtree rectangular grid, and in the hydrodynamic model, a Harten-Lax-Van Leer(HLL) approximate Riemann solver is used to calculate the intercell flux for capturing the dry-to-wet moving boundary. The sediment transport and bed variation equations in a coupled fashion are calculated by including the bed variation and the variable flow density in the flow continuity and momentum equations. The drag force of vegetation is modeled as the sink terms in the momentum equations. The developed model is tested against lab experiments of the dam-break flows over a fix bed and a movable bed in vegetated and non-vegetated channels. The results are compared with experimental data, and good agreement is obtained. It is shown that the reduced velocity under vegetated conditions leads to a decrease of the peak discharge and a rise of the water level of rivers and also an enhancement of the sediment deposition.     

FINITE-VOLUME TVD ALGORITHM FOR DAM-BREAK FLOWS IN OPEN CHANNELS

1 .　INTRODUCTIONThepropagationofborewavesorthemove mentoffreesurfaceflowscausedbydambreak ing ,orsuddenopeningorclosingofasluiceinachannelhasincreasedinterestinenvironmentalandhydraulicengineering .Generallyitcanbede scribedbytheShallowWaterEquations (SWE )throughtheintegrationoftheNavier Stokesequationsoverdepthwiththeassumptionsofhydrostaticpressuredistributionandmildchannel bedslope .ManyclassicaltechniquesthatwereusedforsolvingtheSWEcanbefoundinthepaststudies .However ,whendiscon…     

基于显式有限体积法的一维河网模型

采用显式通量差分裂格式离散圣维南方程组,通过特征线方式处理边界;在局部离散中引入跨临界流熵修正和TVD限制器,以提高模型精度并保证模拟稳定性,最终构建了基于显式有限体积法的一维河网水流模型。经典算例验证表明,所建立的模型能够处理具有激波的跨临界等复杂流态;模型应用于长江南京八卦洲河段,水位和流量的验证表明该模型能够应用于实际的河网,并具有较高的精度,为显式离散方法应用于河网模型提供了一种思路。     

Numerical modeling of dam-break flood through intricate city layouts including underground spaces using GPU-based SPH method

This paper applies the meshfree Smoothed Particle Hydrodynamics （SPH） method with Graphical Processing Unit （GPU） parallel computing technique to investigate the highly complex 3-D dam-break flow in urban areas including underground spaces. Taking the advantage of GPUs parallel computing techniques, simulations involving more than 107 particles can be achieved. We use a virtual geometric plane boundary to handle the outermost solid wall in order to save considerable video card memory for the GPU computing. To evaluate the accuracy of the new GPU-based SPH model, qualitative and quantitative comparison to a real flooding experiment is performed and the results of a numerical model based on Shallow Water Equations （SWEs） is given with good accuracy. With the new GPU-based SPH model, the effects of the building layouts and underground spaces on the propagation of dambreak flood through an intricate city layout are examined.     

Comparison of depth-averaged concentration and bed load flux sediment transport models of dam-break flow

This paper presents numerical simulations of dam-break flow over a movable bed. Two different mathematical models were compared: a fully coupled formulation of shallow water equations with erosion and deposition terms (a depth-averaged concentration flux model), and shallow water equations with a fully coupled Exner equation (a bed load flux model). Both models were discretized using the cell-centered finite volume method, and a second-order Godunov-type scheme was used to solve the equations. The numerical flux was calculated using a Harten, Lax, and van Leer approximate Riemann solver with the contact wave restored (HLLC). A novel slope source term treatment that considers the density change was introduced to the depth-averaged concentration flux model to obtain higher-order accuracy. A source term that accounts for the sediment flux was added to the bed load flux model to reflect the influence of sediment movement on the momentum of the water. In a one-dimensional test case, a sensitivity study on different model parameters was carried out. For the depth-averaged concentration flux model, Manning's coefficient and sediment porosity values showed an almost linear relationship with the bottom change, and for the bed load flux model, the sediment porosity was identified as the most sensitive parameter. The capabilities and limitations of both model concepts are demonstrated in a benchmark experimental test case dealing with dam-break flow over variable bed topography.     

动床条件下溃坝水流的二维水沙耦合模型

现有大部分溃坝水流模型仅适用于模拟定床条件下的水流演进,但溃坝水流经常可在动床条件下演进。因此非常有必要同时模拟溃坝洪水演进时的水沙输移及床面冲淤过程。本文首先建立了动床条件下溃坝水流的二维水沙耦合模型。该模型主要由二维浑水控制方程、非均匀沙不平衡输移方程及河床冲淤方程组成,采用水沙耦合解法以及基于无结构三角网格下的有限体积法离散。同时利用Roe-MUSCL方法以及时间方向的预测-校正格式,使模型在时空方向具有二阶计算精度。然后采用已有算例及水槽试验资料对模型进行了初步验证。最后采用该模型研究了均匀沙及非均匀沙床面对典型溃坝水流演进的影响。模拟结果表明溃坝水流在定床及动床条件下的演进过程明显不同。溃坝水流因流速大,床面变形较快,且床面冲淤速率可与水流变化速率相当,故需要采用浑水控制方程及耦合解法。     

Numerical Simulation of Two-Dimensional Dam-Break Flows in Curved Channels

Two-dimensional transient dam-break flows in a river with bends were theoretically studied. The river was modeled as a curved channel with a constant width and a flat bottom. The water was assumed to be an incompressible and homogeneous fluid. A channel-fitted orthogonal curvilinear coordinate system was established and the corresponding two-dimensional shallow-water equations were derived for this system. The governing equations with well-posed initial and boundary conditions were numerically solved in a rectangular domain by use of the Godunov-type finite-difference scheme, which can capture the hydraulic jump of dam-break flows. The comparison between the obtained numerical results and the experimental data of Miller and Chaudry in a semicircle channel shows the validity of the present numerical scheme. The mathematical model and the numerical method were applied to the dam-break flows in channels with various curvatures. Based on the numerical results, the influence of river curvatures on the dam-break flows was analyzed in details.     

求解对流扩散方程的一种高分辨率有限体积-有限元方法

此文研究在无结构三角网格上求解对流扩散方程的有限体积-有限元方法,设计了一种新的适合于多边形作为控制体的顶点中心型的二维无结构网格方法的vanAlbada型限制器函数,并在此基础上给出了一种新的求解对流扩散方程的有限体积-有限元方法。数值实验结果表明,此文给出的van Albada型限制器函数有效地改进了多边形作为控制体的顶点中心型的有限体积法的收敛性能,给出的求解对流扩散方程的有限体积-有限元方法在精确度上有明显改进。     

浅水流动的模拟方法比较

本文研究浅水模拟中几种具有代表性的计算格式,包括不同阶数的简单格式、迎风格式、利用不同通量控制器的TVD格式以及基于分子运动理论的KFVS格式。通过对具有多种不同水流以及间断的一维溃坝的模拟,这些格式的优劣从各种典型数值现象中体现出来。最后用筛选后的格式对一维溃坝物理实验以及二维扩展渠道水流进行模拟。由于KFVS格式符合基本的流体分子运动规律,虽然引入了一定的耗散误差,但此格式无论对一维问题还是二维问题总体模拟效果都较佳。     

Numerical simulation of shallow-water flooding using a two-dimensional finite volume model

A 2-D Finite Volume Model (FVM) is developed for shallow water flows over a complex topography with wetting and drying processes. The numerical fluxes are computed using the Harten, Lax, and van Leer (HLL) approximate Riemann solver. Second-order accuracy is achieved by employing the MUSCL reconstruction method with a slope limiter in space and an explicit two-stage Runge-Kutta method for time integration. A simple and efficient method is introduced to deal with the wetting and drying processes without any correction of the numerical flux term or the source term. In this new method, a switch of alternative schemes is used to compute the water depths at the cell interface to obtain the numerical flux. The model is verified against benchmark tests with analytical solutions and laboratory experimental data. The numerical results show that the model can simulate different types of flood waves from the ideal flood wave to cases over complex terrains. The satisfactory performance indicates an extensive application prospect of the present model in view of its simplicity and effectiveness.     

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。     

局部断面收缩的溃坝水流三维数值模拟

为研究局部断面收缩对溃坝水流传播的影响,采用压力隐式算子分割法求解雷诺时均方程和RNG k-ε紊流模型,建立了模拟三维局部断面收缩情况下溃坝洪水演进过程的数学模型。采用有限体积法对溃坝水流的控制方程进行离散,利用流体体积函数法处理自由水面,物理变量采用交错网格布置,对局部断面收缩溃坝水流进行数值模拟计算,模拟结果与实体模型试验结果吻合较好。利用该模型研究了溃坝洪水负波的形成和传播过程,得到了负波形成和传播的规律以及溃坝水流的水位变化特征。     

复式断面明渠水流三维数值模拟

复式断面渠道水流流场结构比较复杂,本文用耦合式求解器对复式断面明渠水流的三维流场进行了模拟.采用交错网格,界面上的动量差值采用Roe格式,紊流数学模型选用雷诺应力模型.将计算结果与实验结果进行比较,两者的吻合度较好,从而验证了数学模型的可靠性,最后又对复式断面明渠横剖面上水流运动特性进行了分析.     

溃坝洪水演进平面二维数学模型初步研究

采用逆风格式的有限差分算法,建立了浅水方程的平面二维溃坝洪水演进数学模型。提出了洪水演进计算中“干湿”边界的处理方法,较好地解决了动边界模拟问题。研制了数学模型后处理模块,实现了溃坝洪水演进过程的动态演示。采用Fraccrollo等的部分溃坝模型试验成果对数学模型进行了检验,除溃坝初期在口门附近的水位存在一定差异外,其他位置验证较好。并将该模型应用于天然干河床的洪水演进计算。