A large natural hazard is posed by dam failure and ensuing potentially catastrophic floods downstream, because of the uncontrolled release of the water [1
] stored in the reservoir. To mitigate this impact to the greatest possible degree, it is important to predict the dam-break wave motion by capturing both the temporal and spatial evolutions of floods to manage and reduce the risks caused by flooding [2
] and to predict the propagation process effects of the dam-break waves downstream [3
]. However, predicting these quantities is challenging, and selecting a suitable model to simulate the movement of the dam-break flood accurately and provide useful information on the flow field is therefore an essential step [4
]. The choice of suitable mathematical and numerical models has been shown to be very significant in dam-break flood analyses.
Studies on dam-break flows as conducted in analytical solutions began more than one hundred years ago. Ritter [5
] first derived the earliest analytical solution of the 1D de Saint-Venant equations over a dry bed, Dressler [6
] and Whitham [8
] studied wavefronts influenced by frictional resistance, and Stoker [9
] extended Ritter’s solution to the 1D dam-break problem for a wet bed. Marshall and Méndez [10
] applied the methodology developed by Godunov [11
] for Euler equations of gas dynamics to devise a general procedure for solving the Riemann problem under wet bed conditions. Toro [12
] conducted a complete 1D exact Riemann solver to address both wet- and dry-bed conditions. Chanson [13
] studied the simple analytical solutions for floods originating from sudden dam-breaks using the characteristics method. However, these analytical solutions did not produce accurate results, particularly for wet beds during the initial stages of a dam break [14
Developments from past studies have provided several numerical models aimed at solving the so-called dam break flooding problem [16
], and one-dimensional models, such as Hec-Ras, DAMBRK and MIKE 11, etc. have been used to model dam-break flooding [17
]. Two-dimensional (2D) depth-averaged equations have also been widely used to simulate the dam-break flow problem [18
], and the results show that shallow water equations (SWE) are suitable for representing fluid flows. However, in some cases, the solutions provided by 2D numerical solvers may not be consistent with the experiments, particularly in the near field [23
]. Furthermore, one and two-dimensional models are limited at capturing some details about three-dimensional phenomena [25
]. Several three-dimensional (3D) models based on the Reynolds-averaged Navier-Stokes equations (RANS) have been applied to model dam-break flows in an effort to overcome some of the shortcomings of shallow-water models, which were employed to understand the actual behavior of complex flows during the initial stages of a dam break [26
] and to study dam-break flows resulting from wave impacts on an obstacle or a bottom sill [19
] and turbulent dam-break flow behavior in the near field [4
]. Recently, among the commercially available numerical models, the well-known 3D volume of fluid method (VOF)-based CFD modelling software FLOW-3D has been used widely to analyze unsteady free surface flows, due to the increase in computing power brought about by progress in computer technology. This software calculates numerical solutions to RANS equations using a finite-difference approximation, and it also uses the VOF for tracking the free surface [30
]; it has been used successfully to model dam-break flows [32
However, there are certain hydraulic features of dam break flows over space and time that cannot be captured using 2D shallow-water models. The application of full 3D Navier-Stokes equations for real-life field-scale simulations has a higher computational cost [34
], and the desired outcomes might not yield more accurate results than the shallow-water model [35
]. Therefore, to evaluate both the capability of 3D models and their calculation efficiency, this paper attempts a simplified 3D model-MIKE 3 FM for simulating dam-break flows. The MIKE 3 model has been applied to investigations of several hydrodynamic simulations in natural water basins. It has been used by Bocci et al. [36
], Nikolaos and Georgios [37
] and Goyal and Rathod [38
] for hydrodynamic simulations in field studies. Even with the considerable work of these authors, there have been very few studies on the modelling of dam-breaks using the MIKE 3 FM. In addition, research comparing the performance of 3D shallow water and fully 3D RANS models for solving the problem of dam-break flood propagation has yet to be reported. To fill this gap, the primary objective of the current study is aimed at evaluating simplified 3D SWE, detailed RANS models and analytical solutions for simulating sudden dam-break flows to analyze their accuracy and their applicability to the dam-break problem.
There is a need to validate the numerical models before attempting to perform a hydrodynamic simulation to solve real-life dam-break problems. It is an accepted practice to check numerical models using a set of experimental benchmarks. Limited measured data have been acquired in recent years, due to the difficulties of obtaining field data. This paper draws from the validation proposed by two test cases by Ozmen-Cagatay and Kocaman [30
] and Khankandi et al. [39
]. In the first experiment, which was conducted by Ozmen-Cagatay and Kocaman [30
], there was a dam-break flood wave during the initial stage over different tailwater levels, and it provided measurements of the free surface profiles. Ozmen-Cagatay and Kocaman [30
] compared only the free surface profile calculated by the numerical solutions from the 2D SWE and 3D RANS involving Flow-3D software during the initial stage. During the second experiment, which was designed by Khankandi et al. [39
], measurements from this experiment were used to validate the numerical models aimed at simulating the flood propagation and providing measured data, including free surface profiles during the late stage, time evolutions of the water levels, and velocity variations. A study by Khankandi et al. [39
] primarily focused on the experimental investigation, and it only mentions the water level with Ritter’s solution during the initial stage, because in a 1D analytical solution without boundary conditions (with an infinite channel length both upstream and downstream), it makes no sense to compare the experimental results with the Ritter (dry bed) or Stoker (wet bed) solutions when the reflections from the walls affected the depth profiles, and when further comparisons with numerical simulations for the experiments in Reference [39
] are poor. In aiming directly at these problems, this paper will present a full comparative study on free surface profiles, water depth variations and velocity variations during the entire dam-break process. Here, numerical simulations of the dam break wave are developed using two 3D models for an instantaneous dam break in a finite reservoir with a rectangular channel that is initially dry and wet.
This paper is organized as follows: The governing equations for the two models are first introduced before the numerical scheme is described. The typical simplified test cases were simulated using 3D numerical models and a 1D analytical solution. The model results and the ways in which they compare with the laboratory experiments are discussed, and simulated results of the variations in hydraulic elements over time at different water depth ratios are presented before the conclusions are drawn.
The type of flow model can be classified according to the number of spatial dimensions in the governing equations upon which their predictions are based. A 1D exact solution, a 3D SW model (MIKE 3 FM), and a RANS equation solution with a k–
ε turbulence model (Flow-3D) were tested on typical dam-break flows over dry and wet beds. The validity of the three methods was based on comparisons of the model-calculated results with the laboratory data from Ozmen-Cagatay and Kocaman [30
] and Khankandi et al. [39
]. To better understand the tailwater level effects on the dam-break wave impact, numerical simulations were conducted for different water depth ratios.
The RANS approach reproduced the free-surface profiles of the front wave during the initial stage reasonably well for dry- and wet-bed conditions while the wavefront modelled by the MIKE 3 FM model and 1D analytical solution for the wet-bed case was a bore (i.e., a rectangular jump rather than a curved surface). As time passed, the movement of the front of the flood wave was well simulated by the MIKE 3 FM model. The Flow-3D and MIKE 3 FM models were useful 3D numerical tools for forecasting the temporal variations in the water depth variations and the velocity variation over time for dry and wet beds. However, the 1D analytical solution had a limited practical scope for evaluating the variation in hydraulic features at the full stage of dam-break flow over the dry- and wet-bed and was only applicable during the steady stage. The Flow-3D and MIKE 3 FM numerical methods presented here are suitable for fully hydrodynamic simulations of 3D dam-break flows.
Only idealized 1D dam-break flow cases are examined in this study, and the comparison made here between MIKE 3 FM and RANS models for simulating three-dimensional dam-break flood flows that can be addressed reveal their respective limitations within the dam-break problem. These two 3D models are able to provide complete and detailed information on the physical quantities of dam break flows over space and time that provide information on the dam-break flood evolution, especially in terms of the free surface profile, water depth and flow velocity. At approximately one order of magnitude greater in terms of computation time than the MIKE 3 FM model, the Flow-3D model is much more complicated and time-consuming to use. Therefore, the Flow-3D is more specifically suited to small-scale simulations with a focus on details, and it could be used for the analyses of small areas when knowledge of the 3D structure of the flow is available. In spite of the shortcomings of the MIKE 3 FM approach when applied to dam break problems during the initial stage, this model is more suitable for the large computational domains used in actual problems.