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Sull'onda conseguente al crollo di uno sbarramento in alveo pendente: soluzione perturbativa in assenza di resistenza
No full textRENDICONTI DELL'ISTITUTO LOMBARDO, ACCADEMIA DI SCIENZE E LETTER
New formulation of the two-dimensional steep-slope shallow water equations. Part II: Numerical modeling, validation, and application
No full textNumerical models based on the two-dimensional (2D) shallow water equations (SWE) are commonly used for flood hazard assessment, although the basic assumption of small bottom slopes is not always strictly satisfied, such as in mountain areas. When terrain slopes are large, the steep-slope shallow water equations (SSSWE) are theoretically more suitable because the restrictive hypothesis of small bottom slopes is not introduced in deriving these equations. A new formulation of the 2D SSSWE, in which the water depth is measured in the vertical direction, and the flow velocity is assumed parallel to the bottom surface, is proposed in the companion paper (Part I). The pressure distribution on the vertical is assumed linear (yet non-hydrostatic), and the effect of flow curvature is neglected. In this paper, the new SSSWE are solved with an explicit MUSCL-type second-order accurate finite volume scheme using the centered FORCE method for flux evaluation. The SSSWE model is validated against existing experimental data of one-dimensional (1D) dam-break flows on sloping channels with fixed slopes. The numerical results of the SSSWE and SWE models are compared both in this benchmark test case and in other numerical tests, including a 1D dam-break flow moving on an adverse slope, a 2D dam-break flow spreading on an inclined plane, and a 2D dam-break flow propagating in a sloping parabolic channel. Finally, the two models are applied to the real-field test case of the Cancano dam (Adda River, northern Italy), which is characterized by very steep and irregular topography, especially in the upper portion of the valley. The results show that, on the whole, the SSSWE are more accurate in describing dam-break flows over steep topographies than the conventional SWE and predict less severe flooding with slower wave propagation. The two models are practically equivalent when bottom slopes are relatively small
Three-Dimensional Numerical Modelling of Real-Field Dam-Break Flows: Review and Recent Advances
No full textNumerical modelling is a valuable and effective tool for predicting the dynamics of the inundation caused by the failure of a dam or dyke, thereby assisting in mapping the areas potentially subject to flooding and evaluating the associated flood hazard. This paper systematically reviews literature studies adopting three-dimensional hydrodynamic models for the simulation of large-scale dam-break flooding on irregular real-world topography. Governing equations and numerical methods are analysed, as well as recent advances in numerical techniques, modelling accuracy, and computational efficiency. The dam-break case studies used for model validation are highlighted. The advantages and limitations of the three-dimensional dam-break models are compared with those of the commonly used two-dimensional depth-averaged ones. This review mainly aims at informing researchers and modellers interested in numerical modelling of dam-break flow over real-world topography on recent advances and developments in three-dimensional hydrodynamic models so that they can better direct their future research. Practitioners can find in this review an overview of available three-dimensional codes (research, commercial, freeware, and open-source) and indications for choosing the most suitable numerical method for the application of interest
Modellazione numerica dell’onda conseguente all’ipotetico crollo della prima diga di Cancano
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Dam-Break Wave Propagation in Alpine Valley with HEC-RAS 2D: Experimental Cancano Test Case
Full text linkFlood modeling by numerical solution of the two-dimensional (2D) shallow-water equations is ordinary practice. HEC-RAS 2D was recently released along with a suite of test cases showing the very good performance of the code in many practical situations. However, validation test cases aimed at demonstrating the capability of the software to deal with dam-break floods on very steep and irregular bathymetries are very limited. This paper tests HEC-RAS 2D against the discharge hydrographs measured in a historical physical model built in Froude similitude to analyze the consequences of the hypothetical collapse of the Cancano I dam (northern Italy) and the propagation of the resulting dam-break wave along the 15-km reach of the downstream alpine valley. The experimental hydrographs and the measured extent of the flooded areas are well reproduced by the numerical simulations. Moreover, the results obtained with HEC-RAS 2D are in very good agreement with those obtained using TELEMAC 2D, which confirms the suitability of the HEC-RAS 2D software for dam-break flood studies in steep alpine valleys. The data of the test case are made available to the scientific community for validation purposes
New formulation of the two-dimensional steep-slope shallow water equations. Part I: Theory and analysis
Full text linkTwo-dimensional (2D) depth-averaged shallow water equations (SWE) are widely used to model unsteady free surface flows, such as flooding processes, including those due to dam-break or levee breach. However, the basic hypothesis of small bottom slopes may be far from satisfied in certain practical circumstances, both locally at geometric singularities and even in wide portions of the floodable area, such as in mountain regions. In these cases, the classic 2D SWE might provide inaccurate results, and the steep-slope shallow water equations (SSSWE), in which the restriction of small bottom slopes is relaxed, are a valid alternative modeling option. However, different 2D formulations of this set of equations can be found in the geophysical flow literature, in both global horizontally-oriented and local bottom-oriented coordinate systems. In this paper, a new SSSWE model is presented in which water depth is defined along the vertical direction and flow velocity is assumed parallel to the bottom surface. This choice of the dependent variables combines the advantages of considering the flow velocity parallel to the bottom, as can be expected in gradually varied shallow flow, and handling vertical water depths consistent with elevation data, usually available as digital terrain models. The pressure distribution is assumed linear along the vertical direction and flow curvature effects are neglected. A new formulation of the 2D depth-averaged SSSWE is derived, in which the two dynamic equations represent momentum balances along two spatial directions parallel to the bottom, whose horizontal projections are parallel to two fixed orthogonal coordinate directions. The analysis of the mathematical properties of the new SSSWE equations shows that they are strictly hyperbolic for wet bed conditions and reduce to the conventional 2D SWE when bottom slopes are small. Finally, it is shown that the SSSWE predict a slower flow compared with the conventional SWE in the theoretical case of a 1D dam-break on a frictionless channel with fixed slope. The capabilities of the proposed model are demonstrated in a companion paper on the basis of numerical and experimental tests
Validation of Synthetic Design Hydrographs through 2D hydrodynamic modelling
No full textThe procedure for the determination of Synthetic Design Hydrographs (SDHs), proposed in previous works, is validated by comparing the peak discharges obtained by routing a long series of historical floods and the synthetic floods at different stations along a complex river system.
At this aim, the 60 km long terminal stretch of the Dora Baltea river (Northern Italy) has been modelled according to fully 2D high resolution hydrodynamic approach. The fluvial branch is of considerable complexity due to a strong contraction induced by the presence of a narrow Roman bridge, which, during the most important flood events, causes the reactivation of a paleochannel and the flooding of a part of the city of Ivrea. The hydraulic model has been calibrated on the basis of the main historical floods. Then, all the historical floods over a period of more than 80 years (1939–2020) and the SDHs derived by the same series have been routed. Historical and synthetic peak discharges at two downstream stations have been then compared in probability plots. The results show that the peak discharge distributions derived by routing the historical floods and the SDHs compare well. This suggests that SDHs construction procedure is reliable and has statistical significance
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