Numerical Simulation of Dam-Break Flows Using Radial Basis Functions: Application to Urban Flood Inundation

Dam-break flows pose significant threats to urban areas due to their potential for causing rapid and extensive flooding. Traditional numerical methods for simulating these events struggle with complex urban landscapes. This paper presents an alternative approach using Radial Basis Functions to simulate dam-break flows and their impact on urban flood inundation. The proposed method adapts a new strategy based on Particle Swarm Optimization for variable shape parameter selection on meshfree formulation to enhance the numerical stability and convergence of the simulation. The method’s accuracy and efficiency are demonstrated through numerical experiments, including well-known partial and circular dam-break problems and an idealized city with a single building, highlighting its potential as a valuable tool for urban flood risk management.

Analysis on Dam-Breaking Mode of Tangjiashan Barrier Dam in Beichuan County

Tangjiashan landslide is a typical high-speed consequent landslide of medium-steep dip angle. This landslide triggered by earthquake took place in about semi-minute. The relative sliding displacement is 900 meters, so average sliding speed is about 30 meters per second. The longitudinal length of barrier dam which is formed by high-speed landslide along river is 803.4 meters; and maximum width crossing river is 611.8 meters. And its volume is estimated about 20.37 million steres. Through detailed geological investigation of the barrier dam, together with early geological information before earthquake, geological structures of the barrier dam and its stability of upstream and downstream slopes are studied when water level reaches different elevations in condition of continual after shocks with seismic intensity of 7 or 8 Richter scale. On this basis, dam-breaking mode of barrier dam is discussed deeply. Thereby, analytic results provide significant guidance and advices to front headquarters of Tangjiashan barrier dam, so that some proper engineering measures can be implemented and flood discharge can be carried out well.

Coupled 2D Hydrodynamic and Sediment Transport Modeling of Megaflood due to Glacier Dam-break in Altai Mountains,Southern Siberia

One of the largest known megafloods on earth resulted from a glacier dam-break,which occurred during the Late Quaternary in the Altai Mountains in Southern Siberia.Computational modeling is one of the viable approaches to enhancing the understanding of the flood events.The computational domain of this flood is over 9460 km2 and about 3.784 × 106 cells are involved as a 50 m × 50 m mesh is used,which necessitates a computationally efficient model.Here the Open MP(Open Multiprocessing) technique is adopted to parallelize the code of a coupled 2D hydrodynamic and sediment transport model.It is shown that the computational efficiency is enhanced by over 80% due to the parallelization.The floods over both fixed and mobile beds are well reproduced with specified discharge hydrographs at the dam site.Qualitatively,backwater effects during the flood are resolved at the bifurcation between the Chuja and Katun rivers.Quantitatively,the computed maximum stage and thalweg are physically consistent with the field data of the bars and deposits.The effects of sediment transport and morphological evolution on the flood are considerable.Sensitivity analyses indicate that the impact of the peak discharge is significant,whilst those of the Manningroughness,medium sediment size and shape of the inlet discharge hydrograph are marginal.

Analysis of seismic disaster failure mechanism and dam-break simulation of high arch dam

Based on a Chinese national high arch dam located in a meizoseismal region, a nonlinear numerical analysis model of the damage and failure process of a dam-foundation system is established by employing a 3-D deformable distinct element code(3DEC) and its re-development functions. The proposed analysis model considers the dam-foundation-reservoir coupling effect, infl uence of nonlinear contact in the opening and closing of the dam seam surface and abutment rock joints during strong earthquakes, and radiation damping of far fi eld energy dissipation according to the actual workability state of an arch dam. A safety assessment method and safety evaluation criteria is developed to better understand the arch dam system disaster process from local damage to ultimate failure. The dynamic characteristics, disaster mechanism, limit bearing capacity and the entire failure process of a high arch dam under a strong earthquake are then analyzed. Further, the seismic safety of the arch dam is evaluated according to the proposed evaluation criteria and safety assessment method. As a result, some useful conclusions are obtained for some aspects of the disaster mechanism and failure process of an arch dam. The analysis method and conclusions may be useful in engineering practice.

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.

Optimal Evacuation Scheme Based on Dam-Break Flood Numerical Simulation

The optimal evacuation scheme is studied based on the dam-break flood numerical simulation. A three- dimensional dam-break mathematical model combined with the volume of fluid （VOF） method is adopted. According to the hydraulic information obtained from numerical simulation and selecting principles of evacuation emergency scheme, evacuation route analysis model is proposed, which consists of the road right model and random degree model. The road right model is used to calculate the consumption time in roads, and the random degree model is used to judge whether the roads are blocked. Then the shortest evacuation route is obtained based on Dijstra algorithm. Gongming Reservoir located in Shenzhen is taken as a case to study. The results show that industrial area I is flooded at 2 500 s, and after 5 500 s, most of industrial area II is submerged. The Hushan, Loucun Forest and Chaishan are not flooded around industrial area I and II. Based on the above analysis, the optimal evacuation scheme is determined.

Dam-break Modeling in Alpine Valleys

Dam-break analysis is of great importance in mountain environment,especially where reservoirs are located upstream of densely populated areas and hydraulic hazard should be assessed for land planning purposes.Accordingly,there is a need to identify suitable operative tools which may differ from the ones used in flat flood-prone areas.This paper shows the results provided by a 1D and a 2D model based on the Shallow Water Equations(SWE) for dam-break wave propagation in alpine regions.The 1D model takes advantage of a topographic toolkit that includes an algorithm for pre-processing the Digital Elevation Model(DEM) and of a novel criterion for the automatic cross-section space refinement.The 2D model is FLO-2D,a commercial software widely used for flood routing in mountain areas.In order to verify the predictive effectiveness of these numerical models,the test case of the Cancano dam-break has been recovered from the historical study of De Marchi(1945),which provides a unique laboratory data set concerning the consequences of the potential collapse of the former Cancano dam(Northern Italy).The measured discharge hydrograph at the dam also provides the data to test a simplified method recently proposed for the characterization of the hydrograph following a sudden dam-break.

Experimental Study on the Dam-Break Hydrographs at the Gate Location

When studying the dam-break flow phenomenon,the basic hydrodynamic features of the dam-break flow at the gate location should be verified primarily.In this study,laboratory experiments were performed in a rectangular and horizontal flume with the same initial water head setting on the dry and wet downstream bed conditions.Water surface elevation was extracted through image analysis and validated by comparing with the data measured using a wave gauge.Temporal variation of the water surface elevation at the gate location,quantified in terms of high-speed video recorded images,can be divided into three stages,the sharp decreasing stage,the relatively steady stage,and the gradually decreasing stage.Applicability of several classic analytical solutions of the dam-break problem at the gate location was validated using present experimental data.Ritter's solution is effective for the dry bed condition while Stoker's solution could be applied to the wet bed case,and both are only applicable during the steady stage.Lin' solution reproduces the gate-site hydrographs well during both the relatively steady and the gradually decreasing stages,especially for the condition under which the down-upstream water depth ratio is smaller than 0.138.

Numerical Simulation of Dam-Break Flooding of Cascade Reservoirs

Previous studies at home and abroad have mainly focused on single dam-break, and little attention has been paid so far to the dam-break of cascade reservoirs. Multi-source flooding, which can lead to three-dimensional turbulent phenomena and superposition effects, is the main difference between the dam-break of cascade and single reservoirs. Detailed descriptions of the coupled numerical simulation of multi-source flooding have little been reported, and the initial wet riverbed is rarely considered in current models. Therefore, in this paper, a method based on the three-dimensional (Formula presented.) turbulence model coupled with the volume-of-fluid method is proposed to simulate the dam-break flooding of cascade reservoirs. The upstream river, reservoir, and downstream river are connected by the internal boundary method, and the initial conditions, including river flow and reservoir water, are determined according to the results of the numerical simulation. Coupled numerical simulation of different dam-break flooding is then achieved. The present work solves the challenges presented by the enhancement and superposition of natural river flow, upstream flooding, and downstream flooding. This paper provides a theoretical basis for future studies on the dam-break flood routing of cascade reservoirs. © 2017 Tianjin University and Springer-Verlag GmbH Germany

Life Loss Estimation Based on Dam-Break Flood Uncertainties and Lack of Information in Mountainous Regions of Western China

Compared with urban floods, dam-break floods are associated with greater uncertainties, including variable dam-break modes and hydrological characteristics, so conventional flood estimation methods cannot be directly applied in the estimation of dam-break flood loss. In particular, there is scant information regarding the conditions of affected area and hydrological characteristics in southwest China. In this paper, we introduce an integrated model for estimating flood loss that is adapted to the mountainous regions of southwestern China in light of the relative lack of available information. This model has three major components: a basic information model, a dam-routed flood propagation simulation model, and a loss estimation model. We established the basic information model despite the relative lack of available information using 3S technology [remote sensing (RS); geographical information system (GIS); global positioning system (GPS)], data mining technology, and statistical analysis techniques. Our dam-routed flood propagation simulation model consists of major hydrologic processes and their governing equations for flow propagation, which we solve using finite-difference schemes. In this model, the flood propagation area is divided into grids and each grid is determined by the characteristic parameters obtained from the propagation simulation. We present a case study of the Lianghekou hydropower station in Sichuan Province, China to illustrate the practical application of this integrated model for life loss estimation. © 2017, Tianjin University and Springer-Verlag Berlin Heidelberg.

Numerical Study of Dam-Break Induced Tsunami-Like Bore with A Hump of Different Slopes

Numerical simulation of dam-break wave, as an imitation of tsunami hydraulic bore, with a hump of different slopes is performed in this paper using an in-house code, named a Constrained Interpolation Profile （CIP）-based model. The model is built on a Cartesian grid system with the Navier Stokes equations using a CIP method for the flow solver, and employs an immersed boundary method （IBM） for the treatment of solid body boundary. A more accurate interface capturing scheme, the Tangent of hyperbola for interface capturing/Slope weighting （THINC/SW） scheme, is adopted as the interface capturing method. Then, the CIP-based model is applied to simulate the dam break flow problem in a bumpy channel. Considerable attention is paid to the spilling type reflected bore, the following spilling type wave breaking, free surface profiles and water level variations over time. Computations are compared with available experimental data and other numerical results quantitatively and qualitatively. Further investigation is conducted to analyze the influence of variable slopes on the flow features of the tsunami-like bore.

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 onedimensional 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.

EXPERIMENTAL STUDY OF LANDSLIDE DAM-BREAK FLOOD OVER ERODIBLE BED IN OPEN CHANNELS

Large-scale landslide dams may block the river flow and cause inundation upstream, and subsequently fail and result in severe flooding and damage in the downstream. The need for enhanced understanding of the inundation and flooding is evident. This article presents an experimental study of the inundation and landslide dam-break flooding over erodible bed in open channels. A set of automatic water-level probes is deployed to record the highly transient stage, and the post-flooding channel bed elevation is measured. New experimental data resources are provided for understanding the processes of landslide-induced flooding and for testing mathematical rivers models.

EXPERIMENTAL STUDY OF DAM-BREAK FLOW IN CASCADE RESERVOIRS WITH STEEP BOTTOM SLOPE

Dam break can cause a significant disaster in the downstream, especially, in a valley with cascade reservoirs, which would aggravate the disaster extent. The experimental studies of the dam-break flow of cascade reservoirs are few and far between at the present, Most of related studies concern the failure of a single dam.. This article presents an experimental study of the characteristics of an instantly filled dam-break flow of cascade reservoirs in a rectangular glass flume with a steep bottom slope. A new method was used to simulate the sudden collapse of the dam. A series of sensors for automatic water-levels were deployed to record the rapid water depth fluctuation. The experimental results show that, the ratio of the initial water depth of the downstream reservoir to that of the upstream reservoir would greatly affect the flood peak water depth in the downstream reservoir area and in the stream channel behind the downstream dam, while the influence of the dam spacing is insignificant. In addition, the comparison between the single reservoir and the cascade reservoirs shows some difference in the dam-break flow pattern and the stage hydrograph at the corresponding gauging points.

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

A finite-volume Total Variation Diminishing (TVD) scheme is presented formodeling dam-break flows in open channels. This method is used for solving the 2D shallow waterequations on arbitrary quadrilateral meshes, based upon a second-order hybrid TVD scheme with anoptimum-selected limiter in the space discretization and a two-step Runge-Kutta approach in the timediscretization. Verification for a circular dam-break problem is carried out by comparing thepresent results with others and very good agreement is shown. The present algorithm is then used topredict dam-break flow characteristics in open channels such as in furcated channels. Morecomplicated unsteady flow characteristics in these furcated channels than in the regular channelsstudied previously can observed in this work.

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.

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.

HIGH-RESOLUTION SEMI-DISCRETE CENTRAL SCHEME FOR DAM-BREAK PROBLEMS

A numerical model for simulating the dambreak problems was presented. The model was based on a high-resolution semi-discrete central-upwind difference scheme. In order to reduce spurious oscillation, the uniformly non-oscillatory limiter was employed. A third-order total variation diminishing Runge-Kutta method is used for time integration. The main feature of the presented method is its simplicity. It requires no Riemann solvers, no flux splitting and no flux limiter. It is explicit and does not require dimensional splitting for two dimensions. The Simpson quadrature rule was employed to compute the source term. To verify the effectiveness and accuracy of the proposed method, the 1D dambreak, circular dam-break and partial dam-break problems were simulated. The results are shown to be in good agreement with analytical solution and numerical results obtained by other methods.

上下游水深比对溃坝洪水最大波高演进影响

了解溃坝洪水演进过程中最大波高及其衰减过程,对水库下游洪水风险管理具有重要意义。研究基于大尺度水槽(长32 m、宽1 m、高1.2 m)实验,采用波高仪测量了溃坝波演进过程中波高随时间和空间的变化数据,以此研究不同上下游水深比α和坡度S对溃坝洪水最大波高演进形态、波速和衰减率的影响。此外,研究结合数值模拟对溃坝波波高进行了更深入的分析。研究结果表明:溃坝波的演进形态与上下游水深比α之间存在高度相关性,主要表现为两种典型形态:bore wave和undular wave。当上下游水深比α <0.4时,溃坝波以bore wave形式演进且溃坝波迅速爬升到稳定水位,此时溃坝波振幅小,且水面无显著波动;当上下游水深比α≥0.4时,溃坝波以undular wave形式演进且溃坝波会迅速爬升至最大值然后衰减,此时溃坝波振幅较大,且水面出现规则性波动。坡度S和上下游水深比α的变化影响波速和波速增长率。在相同α情况下,坡度S越大则波速和其增长率越大;在相同S情况下,上下游水深比α增大则波速变大且其增长率变小。对上下游水深比α=0.4~0.8的最大波高演进曲线采用Levenberg-Marquardt算法,进行非线性回归分析并构建最大波高衰减公式,同时通过数值模拟在x=21 m处进行验证,结果表明最大波高衰减公式和数值结果吻合良好。当上下游水深比α> 0.4时,溃坝波的最大波高衰减率都表现为首波的衰减率最大,然后衰减率逐渐减小为0。研究成果为深入理解溃坝洪水的演进过程提供重要支撑,同时为构建溃坝洪水灾害学提供理论依据。

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.