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.

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.

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.

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.

Refined mathematical model for the breaching of concrete-face sand-gravel dams due to overtopping failure

Overtopping is one of the main reasons for the breaching of concrete-face sand-gravel dams(CFSGDs).In this study,a refined mathematical model was established based on the characteristics of the overtopping breaching of CFSGDs.The model characteristics were as follows:(1)Based on the Renormailzation Group(RNG)k-εturbulence theory and volume of fluid(VOF)method,the turbulent characteristics of the dam-break flow were simulated,and the erosion surface of the water and soil was tracked;(2)In consideration of the influence of the change in the sediment content on the dam-break flow,the dam material transport equation,which could reflect the characteristics of particle settlement and entrainment motion,was used to simulate the erosion process of the sand gravels;(3)Based on the bending moment balance method,a failure equation of the concrete face slab under dead weight and water load was established.The proposed model was verified through a case study on the failure of the Gouhou CFSGD.The results showed that the proposed model could well simulate the erosion mode of the special vortex flow of the CFSGD scouring the support body of the concrete face slab inward and reflect the mutual coupling relationship between the dam-break flow,sand gravels,and concrete face slabs.Compared with the measured values,the relative errors of the peak discharge,final breach average width,dam breaching duration,and maximum failure length of the face slab calculated using the proposed model were all less than 12%,thus verifying the rationality of the model.The proposed model was demonstrated to perform better and provide more detailed results than three selected parametric models and three simplified mathematical models.The study results can aid in establishing the risk level and devising early warning strategies for CFSGDs.

Potential application of particle based simulations in reservoir security management

In order to model the movement progress in case of risks such as dam collapse and coastal inundation, particle-based simulation methods, including the discrete-element method and smoothed particle hydrodynamics, which have specific advantages in modeling complex three-dimensional environmental fluid and particulate flows, are adopted as an effective way to illustrate environmental applications possibly happening in the real world. The theory of these methods and their relative advantages compared with traditional methods are discussed. Examples of 3-D flows on realistic topography including the flooding of a river valley as a result of a dam collapse and coastal inundation by a tsunami are introduced. Issues related to validation and quality data availability are also discussed. The results show that the simulations provide a valuable insight in a given situation for the security management of reservoir dams. Validation can only be performed where both the initial and final states can be very well characterized.

Solution of shallow-water equations using least-squares finite-element method

A least-squares finite-element method （LSFEM） for the non-conservative shallow-water equations is presented. The model is capable of handling complex topography, steady and unsteady flows, subcritical and supercritical flows, and flows with smooth and sharp gradient changes. Advantages of the model include： （1） sources terms, such as the bottom slope, surface stresses and bed frictions, can be treated easily without any special treatment; （2） upwind scheme is no needed; （3） a single approximating space can be used for all variables, and its choice of approximating space is not subject to the Ladyzhenskaya-Babuska-Brezzi （LBB） condition; and （4） the resulting system of equations is symmetric and positive-definite （SPD） which can be solved efficiently with the preconditioned conjugate gradient method. The model is verified with flow over a bump, tide induced flow, and dam-break. Computed results are compared with analytic solutions or other numerical results, and show the model is conservative and accurate. The model is then used to simulate flow past a circular cylinder. Important flow charac-teristics, such as variation of water surface around the cylinder and vortex shedding behind the cylinder are investigated. Computed results compare well with experiment data and other numerical results.

Least-squares finite-element method for shallow-water equations with source terms

Numerical solution of shallow-water equations （SWE） has been a challenging task because of its nonlinear hyperbolic nature, admitting discontinuous solution, and the need to satisfy the C-property. The presence of source terms in momentum equations, such as the bottom slope and friction of bed, compounds the difficulties further. In this paper, a least-squares finite-element method for the space discretization and θ-method for the time integration is developed for the 2D non-conservative SWE including the source terms. Advantages of the method include： the source terms can be approximated easily with interpolation functions, no upwind scheme is needed, as well as the resulting system equations is symmetric and positive-definite, therefore, can be solved efficiently with the conjugate gradient method. The method is applied to steady and unsteady flows, subcritical and transcritical flow over a bump, 1D and 2D circular dam-break, wave past a circular cylinder, as well as wave past a hump. Computed results show good C-property, conservation property and compare well with exact solutions and other numerical results for flows with weak and mild gradient changes, but lead to inaccurate predictions for flows with strong gradient changes and discontinuities.

Numerical Simulation of Tsunami-Like Wave Impacting on Breakwater by CLSVOF/IB Method

In the current study,the treatment of air/water interface has been made on dam-break induced tsunami-like wave by the Coupled Level Set and Volume of Fluid(CLSVOF)three-dimensional modelling.The overall CLSVOF method adopts a Tangent of Hy-perbola for INterface Capturing(THINC)scheme with the Weighted Linear Interface Calculation(WLIC)and Level Set(LS)function for capturing interface and calculating normal vector,respectively.As far as THINC/WLIC scheme is concerned,since the convection problem of the VOF function can be solved well,the numerical diffusion can be avoided.The spatial terms in the LS equation were discretized by the Optimized Compact Reconstruction Weighted Essentially Non-Oscillatory(OCRWENO)scheme with fourth-order accuracy,which can avoid false oscillation of LS solution.By combining CLSVOF method with Immersed Boundary(IB)method,the simulation of dam-break induced tsunami-like wave impacting on a stationary breakwater can be carried out.Grid sensitivity,mass error and free-surface profile are first calculated for the tsunami-like wave problem to validate the proposed numerical algorithm,which shows excellent agreement between the numerical results and experimental data.Tsunami-like waves with varied tailgater levels are then investigated.Calculations of velocity magnitude,free-surface profile and wave elevation of the tsunami-like wave are conducted to investigate its dynamics and kinematics.

Dam Break Flood Risk AssesSment for Laiyang City

A dam failure analysis was performed for the City of Laiyang to determine the flood inundation extents and the breach velocities of a hypothetical failure of the Muyu Reservoir Dam in Shandong Province, China. The study was carried out in four steps. First, the possible reasons of the dam failure were analyzed, and the extreme hydrological event was identified as the most critical cause Second, a numerical simulation of the dam break flood was performed. The key factors considered in this simulation include the water level at the dam （the check flood water level）, the inflow to the reservoir （the check flood hydrograph）, and two typical structural scenarios （with/without-levees） along the river reach downstream of the reservoir. Third, based on flood simulations, flood hazard risk analysis was conducted and the results indicate that the peak discharge would be over 40,000 m3/s at the breachand over 22,000 m3/s near Laiyang City. As a result, most of the urban area would be flooded; the duration from the beginning of the dam break to the arrival of peak discharge at Laiyang City is less than half an hour. Finally, a plan for integrated dam break flood management was presented to mitigate the flood risk; both available structural and nonstructural measures were proposed according to the situations in the river basin. The main strategic advises include flood emergency planning, flood risk mapping, flood monitoring and early warning system construction, reservoir regulation, and flood risk public awareness.

Ramunion Arrived at the Disaster-Stricken Area of Laos at the First Time

On July 23,a dam-break occurred to the Auxiliary Dam of XePian-XeNamnoy Hydropower Station located in Southern Laos,and 5 billion cubic meters of water flowed out in a few hours,which has caused the most serious flood of the past ten years in Laos and incurred the loss of many lives.

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.