Three-Dimensional Numerical Modelling of Real-Field Dam-Break Flows: Review and Recent Advances

: Numerical 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.


Introduction
Dam-break floods are caused by the uncontrolled release of water stored in a reservoir due to a total or partial collapse of a constructed or natural dam.Such phenomena can result in potentially catastrophic consequences and many more casualties than other kinds of floods and disasters (e.g., [1,2]).Zhang et al. [3] documented 1443 failures of constructed dams and 1044 failures of landslide dams worldwide over the past two centuries and provided a list of the 20 most significant dam failures (each causing more than 500 casualties), resulting in more than 44,000 fatalities.Among these 20 selected dam disasters, the most catastrophic one is the 1975 Banqiao dam failure (China), which led to the inundation of an area of approximately 12,000 km 2 and the loss of more than 26,000 lives, followed by the disasters of the Vajont dam (Italy) in 1963, the South Fork dam (US) in 1889, and the Machhu-II dam (India) in 1979, each with more than 2000 casualties [1,3,4].In addition, dam-break flooding can cause huge economic losses and extensive environmental damage [5].For example, the 1976 Teton dam disaster (US) resulted in only 11 fatalities, but the flood covered an area of 77 km 2 and reached up to 250 km downstream of the dam, causing more than USD 400 million of damage [6].
Accordingly, the assessment of the flooding hazard associated with hypothetical dambreak scenarios has gained great importance and attracted considerable attention in the last decades, both in engineering practice (e.g., [7,8]) and research (e.g., [9][10][11][12]), for dam-break flood risk management, emergency response, and flood hazard mitigation planning.In principle, a dam-break problem can be studied using either an experimental [13] or a mathematical modelling approach [14,15], or both together (e.g., [16]).However, numerical modelling has become attractive and increasingly popular due to its flexibility and cost-effectiveness and the continuous growth of computing capacities, which allows the processing of a large amount of data and solving mathematical models of great complexity and significant predictive capability [17].Moreover, the current availability of several commercial and freeware Computational Fluid Dynamics (CFD) software codes, equipped with friendly interfaces and including effective pre-and post-processing tools, facilitates the diffusion of numerical models in flood hazard analyses [18].The high-cost and timeconsuming complex operations required to carry out accurate laboratory experimentation have determined that the physical modelling approach is currently mainly adopted to obtain experimental data useful for the validation of numerical models [13,14].
Usually, dam-break flood hazard assessment and mapping are performed using depthaveraged two-dimensional (2D) models, which solve the 2D shallow water equations (SWEs) through finite difference, finite volume, or finite element methods (e.g., [15,[19][20][21]) to predict relevant hydraulic quantities associated with flood hazard (namely, maximum flood depth and velocity).Despite the simplifying assumptions underlying the 2D SWEs, there are many computational challenges in numerically solving these equations, such as shock-capturing capability, treatment of wet and dry fronts, treatment of bottom and friction source terms, reproduction of flow regime transitions, and preservation or achievement of stationary or steady-flow conditions.In any case, the SWEs strictly apply to flows with no significant curvature of the free surface and negligible vertical acceleration (and hence with nearly hydrostatic pressure distribution) over small bottom slopes (e.g., [21,22]).However, in gravity-driven geophysical flows, the terrain may be very steep, at least locally, especially in mountain regions or near topographic singularities [23][24][25].Moreover, the hydrostatic pressure assumption is violated in curvilinear flows, which can also occur as a result of dam failures, especially during the first stages of the motion (e.g., [26,27]) or in case the flooding wave propagates in the presence of bends (e.g., [28]), contractions (e.g., [29,30]), bottom singularities (e.g., [31,32]), or obstacles and structures (e.g., [33][34][35]).For example, Figure 1 shows two pictures of the impact of a dam-break wave against a prismatic block [34].Such a physical process is characterised by marked three-dimensional (3D) features.
Water 2023, 15, x FOR PEER REVIEW 2 of 29 dam-break flood risk management, emergency response, and flood hazard mitigation planning.
In principle, a dam-break problem can be studied using either an experimental [13] or a mathematical modelling approach [14,15], or both together (e.g., [16]).However, numerical modelling has become attractive and increasingly popular due to its flexibility and cost-effectiveness and the continuous growth of computing capacities, which allows the processing of a large amount of data and solving mathematical models of great complexity and significant predictive capability [17].Moreover, the current availability of several commercial and freeware Computational Fluid Dynamics (CFD) software codes, equipped with friendly interfaces and including effective pre-and post-processing tools, facilitates the diffusion of numerical models in flood hazard analyses [18].The high-cost and time-consuming complex operations required to carry out accurate laboratory experimentation have determined that the physical modelling approach is currently mainly adopted to obtain experimental data useful for the validation of numerical models [13,14].
Usually, dam-break flood hazard assessment and mapping are performed using depth-averaged two-dimensional (2D) models, which solve the 2D shallow water equations (SWEs) through finite difference, finite volume, or finite element methods (e.g., [15,[19][20][21]) to predict relevant hydraulic quantities associated with flood hazards (namely, maximum flood depth and velocity).Despite the simplifying assumptions underlying the 2D SWEs, there are many computational challenges in numerically solving these equations, such as shock-capturing capability, treatment of wet and dry fronts, treatment of bottom and friction source terms, reproduction of flow regime transitions, and preservation or achievement of stationary or steady-flow conditions.In any case, the SWEs strictly apply to flows with no significant curvature of the free surface and negligible vertical acceleration (and hence with nearly hydrostatic pressure distribution) over small bottom slopes (e.g., [21,22]).However, in gravity-driven geophysical flows, the terrain may be very steep, at least locally, especially in mountain regions or near topographic singularities [23][24][25].Moreover, the hydrostatic pressure assumption is violated in curvilinear flows, which can also occur as a result of dam failures, especially during the first stages of the motion (e.g., [26,27]) or in case the flooding wave propagates in the presence of bends (e.g., [28]), contractions (e.g., [29,30]), bottom singularities (e.g., [31,32]), or obstacles and structures (e.g., [33][34][35]).For example, Figure 1 shows two pictures of the impact of a dambreak wave against a prismatic block [34].Such a physical process is characterised by marked three-dimensional (3D) features.Local 3D effects cannot be reproduced by the 2D SWEs [36], with consequent possible limitations in the predictive capability of 2D shallow-water models and inaccuracies in the prediction of the relevant hydraulic variables, such as flood inundation extent, maximum flood depths, and impact loads on structures [37].More general formulations of the Local 3D effects cannot be reproduced by the 2D SWEs [36], with consequent possible limitations in the predictive capability of 2D shallow-water models and inaccuracies in the prediction of the relevant hydraulic variables, such as flood inundation extent, maximum flood depths, and impact loads on structures [37].More general formulations of the 2D depth-averaged SWEs have been proposed in the literature to overcome this drawback without resorting to more computationally expensive 3D models.In these enhanced formulations, some of the restrictive assumptions of the classic shallow-water model are relaxed Water 2023, 15, 3130 3 of 26 while retaining its robustness and simplicity.For example, steep-slope SWEs (SSSWEs) were introduced to simulate shallow flows over steep terrain (e.g., [24,25,38]).Boussinesqtype models (e.g., [23,39,40]), as well as vertically averaged and moment (VAM) equations (e.g., [41]) or depth-averaged equations incorporating an "enhanced" gravity (e.g., [42,43]), can be used to simulate non-hydrostatic flows, preserving the vertical momentum balance and including the effect of the vertical flow acceleration.
Recent advances in computing performance have fostered the application of 3D numerical models [44], which offer an improved predictive capability [45] and a more accurate description of the flow features, especially where vertical flow acceleration cannot be neglected and the pressure distribution is far from hydrostatic [19].Three-dimensional models with different degrees of complexity (and, consequently, different computational costs) can be used, namely [40] direct numerical simulation (DNS) models, which numerically solve the Navier-Stokes equations (NSEs), resolving all turbulence spatial and temporal scales; large-eddy simulation (LES) models, which solve the filtered NSEs, thus ignoring the smallest length scales; and models that solve the Reynolds-averaged Navier-Stokes equations (RANS), coupled with a closure turbulence model [46].DNS and LES models are significantly more computationally expensive than the RANS ones, especially at the high Reynolds numbers encountered in environmental free-surface flows.Therefore, the application of DNS and LES models in this field is feasible only in limited domains [19].Consequently, RANS solvers are the most common choice for large-scale real-world dambreak flood simulations.However, since the flow depth does not explicitly appear in the basic equations of 3D models, great care has to be devoted to spatial discretization in the vertical direction, and additional computational effort is required for free surface tracking [37].Several free-surface-tracking techniques have been proposed in the literature.The best known are the Volume of Fluid (VOF; [47]) and the Level Set [48] methods (or a combination of the two in coupled Level Set-VOF methods; e.g., [49]).The VOF model is the most popular in dam-break flow simulations [50].An alternative strategy to solve the 3D governing equations, avoiding the construction of a computational mesh and the adoption of complex free-surface-tracking algorithms, is based on meshless particle-based methods, such as Smoothed Particle Hydrodynamics (SPH; [51]), which has also been applied in the modelling of dam-break flow (e.g., [52,53]), even on real-world topography, and other environmental applications [54,55].
However, the high computational cost of 3D models is still a significant limitation, especially in large-scale field studies or when high spatial accuracy is required.This limitation has hindered the diffusion of 3D models in the past for real-field applications, favouring the 2D depth-averaged ones.Hence, high-performance computing, such as parallel or Graphics Processing Unit (GPU) computing, is today a valuable support to enhance the computational efficiency of 3D models and reduce computational time.
Dam-break models (both 2D and 3D) are usually validated against experimental data of laboratory test cases [13], which, however, are typically schematic (e.g., [44,56]) or include isolated singularities (e.g., [50,[57][58][59]).Instead, real dam-break events involve irregular topography and constitute far more challenging benchmarks for numerical models.However, well-documented historical dam-break events are scarce and often characterised by uncertain available information [14], making their use arduous for complete validation of the numerical models (especially for 3D ones, in which several parameters are involved).Nonetheless, they provide valuable information about the different degrees of reliability of the models in reproducing dam-break flow features over real-world topography.
Table 1 provides a comparative summary of the advantages and shortcomings of 3D and depth-averaged 2D models.Given the increasing diffusion of 3D CFD models and their improved predictive capabilities compared with the 2D ones, this review focuses on 3D modelling of large-scale real-field dam-break floods.Figure 2 shows a sketch of the methodological framework of this study.The systematic review is restricted to publications focusing on 3D CFD modelling of dam-break flow and providing application examples of numerical simulation of dam-break flooding over irregular real-world topography.A comparative analysis is performed on the documents collected, and the information relevant to 3D CFD modelling is reported in tabular form (Section 2).The results of the analysis allow statistical information on key items of the reviewed documents (such as year of publication, software status, model type, and numerical scheme) to be obtained.The discussion of the review findings is centred on the following aspects: improvements in simulation accuracy, model validation and calibration, improvements in computational efficiency, and improvements in result visualization (Section 3).Finally, conclusions are drawn, outlining implications that can facilitate practical applications and future research on 3D CFD models for the simulation of large-scale dam-break flooding on irregular real-world topography (Section 4).
their improved predictive capabilities compared with the 2D ones, this review focuses on 3D modelling of large-scale real-field dam-break floods.Figure 2 shows a sketch of the methodological framework of this study.The systematic review is restricted to publications focusing on 3D CFD modelling of dam-break flow and providing application examples of numerical simulation of dam-break flooding over irregular real-world topography.A comparative analysis is performed on the documents collected, and the information relevant to 3D CFD modelling is reported in tabular form (Section 2).The results of the analysis allow statistical information on key items of the reviewed documents (such as year of publication, software status, model type, and numerical scheme) to be obtained.The discussion of the review findings is centred on the following aspects: improvements in simulation accuracy, model validation and calibration, improvements in computational efficiency, and improvements in result visualization (Section 3).Finally, conclusions are drawn, outlining implications that can facilitate practical applications and future research on 3D CFD models for the simulation of large-scale dam-break flooding on irregular real-world topography (Section 4).

Motivations of the Present Review
There is a vast literature overviewing, describing, comparing, and evaluating flood inundation numerical models for flood risk assessment and water resources management (e.g., [15,18,19]).For instance, Teng et al. [15] conducted a comprehensive review of different modelling approaches (empirical, hydrodynamic, and simplified conceptual models), highlighting their advantages and drawbacks and discussing the sources of uncertainty in flood inundation modelling.Mudashiru et al. [18] provided a similar overview, focusing on flood hazard mapping.Bates [19] surveyed recent advances in floodplain inundation modelling, discussing the ability of the numerical models to reproduce the physical aspects of the flooding process.Luo et al. [60] and Mignot and Dewals [61] limited the area of focus, reviewing specifically urban flood simulation models and analysing their hydrologic and hydrodynamic component modules.More recently, Kumar et al. [62] and Avila-Aceves et al. [63] offered a broad overview of different modelling approaches and numerical techniques for simulating large-scale inundations, providing insight into their strengths and weaknesses.
Only some of the previously mentioned reviews mention the use of 3D hydrodynamic models for flood inundation simulations [15,19].However, to our knowledge, no

Motivations of the Present Review
There is a vast literature overviewing, describing, comparing, and evaluating flood inundation numerical models for flood risk assessment and water resources management (e.g., [15,18,19]).For instance, Teng et al. [15] conducted a comprehensive review of different modelling approaches (empirical, hydrodynamic, and simplified conceptual models), highlighting their advantages and drawbacks and discussing the sources of uncertainty in flood inundation modelling.Mudashiru et al. [18] provided a similar overview, focusing on flood hazard mapping.Bates [19] surveyed recent advances in floodplain inundation modelling, discussing the ability of the numerical models to reproduce the physical aspects of the flooding process.Luo et al. [60] and Mignot and Dewals [61] limited the area of focus, reviewing specifically urban flood simulation models and analysing their hydrologic and hydrodynamic component modules.More recently, Kumar et al. [62] and Avila-Aceves et al. [63] offered a broad overview of different modelling approaches and numerical techniques for simulating large-scale inundations, providing insight into their strengths and weaknesses.
Only a few of the previously mentioned reviews touch on the use of 3D hydrodynamic models for flood inundation simulations [15,19].However, to our knowledge, no literature reviews exist on the specific topic of 3D hydrodynamic modelling of large-scale dam-break flows on real-world topography.Recent advances in 3D dam-break modelling, the growing attention given to 3D CFD models in recent times due to enhanced computational efficiency, and the prospect of using 3D models extensively in engineering practice in the near future for dam-break flood risk assessment are the main motivations for this review.

Objectives of the Present Review
This review aims to inform researchers new to the field and more experienced researchers of the recent advances in 3D CFD dam-break modelling on real-world topography, thereby enabling them to have a general, updated overview of this topic.The comparative analysis of the relevant references selected can help modellers, practitioners, emergency response agencies, and dam owners remain up to date on the latest developments in dam-break simulation tools and choose the most suitable numerical model for the specific application of interest.Finally, this review study provides state-of-the-art information to direct future research on 3D dam-break numerical modelling for real field applications.

Review and Comparative Analysis
A systematic and careful search was performed in the most well-known scientific databases (based on the keywords: "dam-break", "3D numerical modelling", "real topography", "complex topography", and similar) to ensure wide coverage of the existing literature on 3D numerical modelling of large-scale dam-break flows over real-world topography.Mainly the academic literature (i.e., journal or conference articles) was considered; the grey literature was not included.
The documents retrieved in the literature survey are arranged in Table 2, including studies on dam spillway flows or overtopping flows reporting the numerical simulation of the subsequent flood propagation downstream.Table entries are organised in chronological order.References that contain multiple real-world case studies are repeated for each of these and appear in different rows of the table (i.e., one row for each case study).
Table 2 provides the following, most significant information.
(1) Relevant references retrieved.Multiple references are reported in the same table row when details providing a complete description of the case study analysed can be obtained from various articles.In the case of duplicate studies, the most complete one was considered, and subordinately, the earliest one.
(3) Basic equations of the simulation models: in order of increasing complexity, the Euler equations, the Navier-Stokes equations, and the RANS equations for incompressible flow.In the last case, a closure turbulence model is coupled with the governing equations.Lattice Boltzmann methods (based on the Boltzmann equation and simulating the flow through collision models of fictitious particles moving on a discrete lattice grid) are used more rarely in dam-break flooding simulations.The table also reports the rheological model coupled with the hydrodynamic equations in mudflow modelling of tailings dam breaks and the erosional model used in the analysis of geomorphic dam-break flows over an erodible bottom.
(4) Numerical methods used for spatial and temporal discretization of the model equations.The indication of the numerical scheme used for the simulations is accompanied by the specification of the discretization technique (finite volume, finite element, SPH, etc.).
(5) Dam-break case studies considered to demonstrate the applicability of the numerical models.Some case studies concern historical dam-break events, while others concern hypothetical dam failures.The former case studies, if well documented, can be used for model validation and to evaluate the model's ability to reproduce real-field dam-break flooding.Case studies of the latter type concern model applications to real-world situations, mainly aimed at assessing dam-break flood hazards in potentially floodable areas.
(6) Details about the computational domain and the spatial resolution adopted in the numerical simulation of the case studies considered (i.e., the number of grid cells in mesh-based models or fluid particles in meshless models).The mesh type (structured or unstructured) and the shape of the grid elements are specified for mesh-based models.
(7) Outcomes of the numerical modelling.Typically, model results include flooded areas, flood depth contour maps and flow velocity fields at selected times, contour maps of the maximum values of flood depth and velocity magnitude, time series of flood depth and flow velocity at given locations, and time series of flow discharge at selected cross-sections.
(8) Focus of the studies.The focus may be on the model validation, the prediction or reconstruction of the inundation dynamics, or the 3D effects due to flow curvature.Different aspects are sometimes examined contextually.
(9) Computational efficiency.The simulation (physical) time and the corresponding computational run-time are reported for the case studies (when these data are available), along with strategies implemented to improve computational efficiency.(10) Publication year.This bibliographic information is useful to place each contribution in time, outlining the evolution of the numerical models over time and research trends.If multiple references are associated with a single table row, the publication year of the oldest one is reported. (

Results and Discussion
A total of 34 documents relating to the period from 2006 to the present were retrieved from the literature review.However, 39 entries appear in Table 2, as nine of the references examined present two different case studies, hence being repeated in two different table rows, and four references are mentioned together with other works that contain identical case studies.
Figure 3 summarises the main statistical information derived from the analysis of the papers reviewed.About a third of these (12) were published in the last three years (2020-2022), confirming a recent growing interest in 3D modelling of real-field dam-break flows (Figure 3a).In most case studies examined (43.6%), in-house research codes were adopted for the numerical analyses; commercial CFD software packages and open-source or freeware codes were used in 17.9% and 35.9% of cases, respectively (Figure 3b).The type of code was unspecified in only one case.Mesh-based methods appear in Table 2 more times (25) than particle-based ones (14) (Figure 3c).Among the former methods, the VOF-based finite volume ones are the most commonly used, whereas, among the latter, the SPH methods are prevalent.This state of the art was also observed by other researchers (e.g., [101]) who, in addition, showed how numerical results obtained from these two methods are in good agreement [102].The Lattice Boltzmann method appears in Table 2 in only one case.This modern numerical technique still has limited application to dam-break problems [103,104].Finite volume techniques are the most used in the reviewed papers for discretizing the governing equations in mesh-based models (Figure 3d).Indeed, the finite volume method is particularly suitable for solving conservation law equations because it exploits the integral formulation of the equations to capture their weak solutions [105].Finite element methods appear fewer times in Table 2, since this numerical technique still constitutes a developing research area in CFD [106] and free surface flow modelling [107], despite its ability to treat complex geometries and reach high-order accuracy.

Results and Discussion
A total of 34 documents relating to the period from 2006 to the present were retrieved from the literature review.However, 39 entries appear in Table 2, as nine of the references examined present two different case studies, hence being repeated in two different table rows, and four references are mentioned together with other works that contain identical case studies.
Figure 3 summarises the main statistical information derived from the analysis of the papers reviewed.About a third of these (12) were published in the last three years (2020-2022), confirming a recent growing interest in 3D modelling of real-field dam-break flows (Figure 3a).In most case studies examined (43.6%), in-house research codes were adopted for the numerical analyses; commercial CFD software packages and open-source or freeware codes were used in 17.9% and 35.9% of cases, respectively (Figure 3b).The type of code was unspecified in only one case.Mesh-based methods appear in Table 2 more times (25) than particle-based ones (14) (Figure 3c).Among the former methods, the VOFbased finite volume ones are the most commonly used, whereas, among the latter, the SPH methods are prevalent.This state of the art was also observed by other researchers (e.g., [101]) who, in addition, showed how numerical results obtained from these two methods are in good agreement [102].The Lattice Boltzmann method appears in Table 2 in only one case.This modern numerical technique still has limited application to dambreak problems [103,104].Finite volume techniques are the most used in the reviewed papers for discretizing the governing equations in mesh-based models (Figure 3d).Indeed, the finite volume method is particularly suitable for solving conservation law equations because it exploits the integral formulation of the equations to capture their weak solutions [105].Finite element methods appear fewer times in Table 2, since this numerical technique still constitutes a developing research area in CFD [106] and free surface flow modelling [107], despite its ability to treat complex geometries and reach high-order accuracy.The catastrophic scenario of the sudden and total dam collapse is mostly considered in the case studies reviewed, thus neglecting the breach development dynamics.The catastrophic scenario of the sudden and total dam collapse is mostly considered in the case studies reviewed, thus neglecting the breach development dynamics.

Improvements in Simulation Accuracy
Three-dimensional hydrodynamic modelling improves the mathematical description of dam-break flows compared to routinely adopted 2D depth-averaged modelling, because 3D models overcome the intrinsic limitations of 2D ones.Therefore, 3D modelling is of wide applicability and general interest in dam-break problems.Indeed, 3D models calculate the pressure field and include the vertical fluid acceleration, thereby inherently taking into account the effects of flow curvature.Moreover, 3D models involve the vertical velocity component and describe the vertical variation of flow velocity.Conversely, 2D depthaveraged models introduce hypotheses on the vertical pressure distribution (assumed hydrostatic in SWE models) or the shape of the vertical velocity profile in non-hydrostatic flow models [23].Finally, 3D models can include vertical turbulence and spiral flows [60] and can correctly simulate the impact of flows against obstacles or structures [109,110].These enhanced modelling capabilities of 3D models can ensure more accurate flow predictions, especially around structures, at topographic singularities where sudden changes in the bottom surface occur, and in urban flooding simulations.Reproducing small-scale eddies, vertical turbulence, and residual circulation can be crucial for accurately predicting both near-field and far-field features of the flooding dynamics and the flow variables involved in flood hazard assessments.
The capabilities of 3D models were verified and validated in most of the articles reviewed, but the analysis of 3D flow effects is the focus of only a few of them (e.g., [70,71,82,87]).For example, Biscarini et al. [82] discussed the 3D effects induced on a dam-break flow by a sharp river bend.Even fewer are the articles that, based on a real-field case study, compare the results obtained through a 3D model with those obtained through a standard 2D depthaveraged shallow-water model, analysing the differences [37,50,80].For example, Munoz and Constantinescu [37], studying the flood inundations induced by the hypothetical failure of two flood-protection dams in the United States, found that their 2D depth-averaged model underpredicted the wave propagation speed and the inundation extent compared with a 3D model.Most frequently, in the literature, the comparison of 3D and 2D model performance in predicting dam-break flow was made on the basis of schematic test cases characterised by a simple geometry (e.g., [27,111]).
In 3D models based on the RANS equations, the effect of turbulence is introduced through a closure turbulence model.The classic k-ε model is the most adopted in the references reviewed (entries [37,82,85,95] in Table 2).However, no systematic sensitivity analyses on the turbulence model type were performed for real-world dam-break case studies.The prediction capabilities of different turbulence models were typically compared again on the basis of dam-break test cases characterised by a simple and schematic geometry (e.g., [110,[112][113][114][115][116]), exploiting laboratory experimental data.Some references analysed in this review consider mudflows resulting from a tailings dam failure.In these studies, the tailings slurry is assumed as a homogeneous non-Newtonian viscoplastic fluid, and a suitable constitutive equation is added to the set of governing equations to characterise its rheological properties [88,91,92,99,100].In some other studies among those reviewed, non-Newtonian rheological models are used to describe the behaviour of moving sediment layers in the path of the dam-break wave [90,98], thereby simulating the geomorphic effects produced by a dam-break flood on an erodible bed.An erosional dam break (with bed-load transport) on real-world topography was modelled by Amicarelli et al. [84] through an SPH model applied to a mixture of water and a non-cohesive granular material.
Recently, topographic data accuracy and spatial resolution have been significantly improved thanks to highly accurate terrain surveying techniques, such as scanning airborne laser altimetry (LIDAR), which can reach a horizontal resolution even below 1 m and a vertical accuracy of 10 −1 m [19], and unmanned aerial vehicle (UAV) photogrammetry, which is very effective in terms of timeliness, repeatability, and high resolution [91].Hence, highly accurate and high-resolution topographic digital models are widespread nowadays, even in urban areas [85], and allow for very accurate dam-break flow modelling.
On the other hand, despite the implicit greater descriptive capacity (and complexity) of 3D models, accuracy improvement in 3D numerical predictions compared with simpler, low-dimensional models may be illusory if topographic and input data are limited and inaccurate and reliable real-field validation data are scarce [19,117].

Model Validation and Calibration
Dam-break models are usually validated by comparing numerical results with experimental data [13].To this end, real-field data of historical dam-break events or experimental data obtained from small-scale physical models with an irregular bottom can be very useful [14], especially if the numerical model will be used in practical engineering applications for dam-break inundation mapping and flood hazard assessment.Validation against real-field data can also help discriminate among potential competing models able to return plausible and realistic results.
Based on the articles reviewed, the most used real-field test case for validating 3D dam-break numerical models is the historical event of the 1959 Malpasset dam break (entries [75,82,83] in Table 2).An extensive database is available for this test case, including field data collected immediately after the event and data measured during a laboratory investigation in a reduced-scale physical model [118,119].However, other historical dambreak events are well documented [14]; for some of these, the test case and the experimental data (from field surveys or consultation of historical documents) are available in digital format [120,121].
Another test case frequently used for validating 3D dam-break numerical models is the Toce River test case (entries [50,81,85,96] in Table 2), which concerns a dam-break-like flash flood induced by imposing an inflow discharge hydrograph in a 1:100 physical model of a 5 km long stretch of the Toce River valley in northern Italy [122].An idealised urban district was inserted in this physical model to simulate the dam-break flooding of an urban area.Other experimental data from reduced-scale physical models are available in the literature [123,124] and could be considered for validating 3D dam-break models.
In complex 3D models, a large number of model parameters requiring calibration appear, mainly concerning numerical schemes and turbulence models.Accordingly, an optimization process involving many parameters should be performed, which might be challenging and computationally expensive due to the long runtime of each model execution.Therefore, calibration parameters are usually set based on expert judgement, according to the suggestions of software users' guides or following the choices made in similar numerical studies.
Uncertainty analysis is widely recognised as desirable, if not indispensable, in environmental system modelling to associate uncertainty estimates with model predictions [15].In real-world applications of dam-break inundation modelling, the main uncertainty sources are topographic input data, model parameters (including the mesh resolution), and initial conditions defining the dam-break scenario (i.e., breach parameters and reservoir filling conditions).Modern remote sensing acquisition technologies (such as LIDAR) have drastically reduced the uncertainty in terrain description, and the availability of high-resolution topographic data makes it possible to include in the computational domain obstacles, structures, and topographic details that may significantly influence the inundation process [60].The typical way to individually quantify the effects of model or scenario parameters on numerical predictions is to perform a sensitivity analysis based on a sampling approach (e.g., [125,126]).Monte Carlo methods are usually adopted to this end, considering a sample of the appropriate size to ensure convergence.However, exhaustive sensitivity analyses based on large sets of parameter values (and, consequently, many model runs) may be prohibitive using 3D hydrodynamic models.To overcome this limitation, Rizzo et al. [10] (who, however, used a 2D depth-averaged shallow-water model) proposed a probabilistic method based on a limited set of dam-break scenarios, each of which had a (conditional) probability associated with it.As regards the spatial resolution, Zhang et al. [87] performed a sensitivity analysis on the mesh size for a realistic dike-break flooding case, concluding that the spatial resolution significantly impacts the accuracy of model results when the terrain is irregular, as in real-field applications.

Improvements in Computational Efficiency
The main reason for the limited use of 3D models in large-scale dam-break flood simulation over real-world topography is that they are time-consuming due to their high computational cost, which depends on various factors, such as the complexity of the numerical method adopted to solve the governing equations, the extent of the computational domain, the simulation (physical) time (usually set long enough to reconstruct the salient features of the flooding process), and the mesh type and resolution (in mesh-based models) or the particle size (in particle-based models).This problem-which is exacerbated in real-world applications-does not concern, as a rule, dam-break tests characterised by a schematic geometry (i.e., verification against analytical solutions or validation against laboratory data), because such simple tests do not require, in general, significant computational resources.
A viable option to overcome the limitation related to computational efficiency without resorting to approximate models [127] is to accelerate 3D model calculations via highperformance computing and GPU technology to reduce model running times [19].In particular, parallel computing is a valid and widely used method to improve computational efficiency, possibly exploiting GPU computing power and processing capabilities.
Reducing the computational time of model executions also allows larger domains to be considered with high spatial resolution, extending the simulation of the flooding dynamics for a longer simulation time.Moreover, a large set of dam-break scenarios can be used in sensitivity analyses for assessing model uncertainty.
Table 2 shows that parallelization techniques based on Message Passing Interface (MPI; [39,72]) and the GPU implementation of the simulation model [77,86,91] were used in 3D modelling of real-field dam-break flows.The ratio of model run time to simulation time is highly variable, ranging from 10 2 to 10 4 , depending on the number of processors and the total number of computational cells or particles.Yu et al. [92] analysed the gain in parallel speed-up as a function of the number of processors.

Improvements in Result Visualization
Geographic information systems (GISs; [72,73]) and 3D virtual geographic environment (VGE) systems have recently become attractive tools for the 3D dynamic visualization of model results, improving the communication of the dam-break flooding dynamics and the potential consequences (e.g., [128]).The availability of 3D numerical results facilitates the development of 3D virtual reality environments and visualizations, which, currently, are usually based on 2D hydraulic model data and results extrapolated into 3D (e.g., [129,130]).

Conclusions
Three-dimensional numerical modelling of dam-break flow has developed considerably in the last decade thanks to the significant increase in the available computing resources, which has made 3D modelling a viable alternative to routinely used 2D depthaveraged modelling in large-scale real-field applications, despite its higher computational cost.Even if 3D numerical models have only recently become a real and feasible option in large-scale dam-break modelling on real-world topography, we found in the literature a noticeable number of contributions concerning this fluid dynamic application, including standard dam-break water flows as well as geomorphic and tailings dam-break flows.Mesh-based models are mostly used for solving the governing hydrodynamic equations, which are the Navier-Stokes equations or the RANS equations coupled with a free-surface tracking technique (e.g., the VOF method) and a closure turbulence model.However, in recent years, particle-based models based on the SPH technique have become widespread in computational fluid dynamics and in the simulation of dam-break flows.Indeed, this method benefits from both being mesh-free and not requiring computationally expensive free-surface tracking techniques.The application of the Lattice Boltzmann method to large-scale 3D dam-break flood modelling is a relatively new research field that deserves further exploration [96].
This paper systematically reviews the state-of-the-art 3D numerical modelling of large-scale dam-break floods on irregular real-world topography.The literature survey is mainly based on journal and conference papers published until July 2023, excluding the grey literature.We aimed to conduct an exhaustive and meticulous review based on comprehensive search parameters and inclusive keywords.Nevertheless, we may have missed studies published in journals of local diffusion or not specifically focused on 3D numerical modelling.
The references reviewed are organised into a table (Table 2) reporting extensive information on numerical models, case studies analysed, research focus, numerical results, and computational efficiency.Recent developments and key improvements in modelling and computational aspects, such as model accuracy and efficiency, are discussed.Regarding computational efficiency, code running on Graphics Processing Units and massive parallelization ensure a significant computational time reduction.This general improvement in computational efficiency allows for high spatial resolutions, even in large-scale applications.However, model calibration remains challenging due to the large number of parameters involved in 3D models, especially when coupled with a turbulence model.The 3D visualization of the numerical results can improve the quality of the communication of the dam-break flood hazard to managers and stakeholders, thus contributing to the mitigation of dam-break flood consequences.
Compared to the less computationally demanding 2D depth-averaged models, the 3D ones allow for a more detailed and accurate prediction of the flooding dynamics, inherently including the fluid vertical acceleration and 3D effects due to the flow curvature induced by the irregular topography.Freeware and commercial CFD software (relatively user-friendly) are available nowadays for dam-break flow analysis, even concerning large-scale problems on real-world topography.
Future research may concern coupled 2D-3D models as a valid compromise between simulation accuracy and computational efficiency.This modelling option is currently already introduced in some CFD software (e.g., [131]) in order to simulate large-scale flows in which the shallow water assumptions are approximately valid with a 2D depth-averaged model, and near-field flows and localised flow features (near structures, obstacles, or significant topographic irregularities) with a 3D model.For instance, hybrid 2D-3D models could be used to simulate dam-break flooding generated by a partial dam failure, with the breach involving only the upper part of the dam.In this case, the weir-type outflow could be modelled by the 3D model and the wave propagation in the downstream area by the 2D depth-averaged model.The portions of the computational domain in which to apply the two different models can be previously identified and efficiently linked.
This review can guide researchers, modellers, and practitioners to compare existing 3D dam-break numerical models, choose the most suitable model for the application of interest, and select state-of-the-art numerical approaches.This review can also support modellers and researchers, providing a basis for future research in 3D simulation models and computational techniques for dam-break flow modelling, with special attention to large-scale real-field applications.

Figure 1 .
Figure 1.Three-dimensional features of a dam-break wave impacting a structure.The pictures were taken during the laboratory investigation performed by Aureli et al. [34].Time t commences with the sudden gate removal.

Figure 1 .
Figure 1.Three-dimensional features of a dam-break wave impacting a structure.The pictures were taken during the laboratory investigation performed by Aureli et al. [34].Time t starts from the sudden gate removal.

Figure 2 .
Figure 2. Schematic of the methodological framework of this review study.

Figure 2 .
Figure 2. Schematic of the methodological framework of this review study.

Figure 3 .
Figure 3. Statistical information from the database of the reviewed papers on 3D modelling of largescale real-world dam-break floods: (a) year of publication; (b) status of the software; (c) model type; (d) numerical scheme.

Figure 3 .
Figure 3. Statistical information from the database of the reviewed papers on 3D modelling of large-scale real-world dam-break floods: (a) year of publication; (b) status of the software; (c) model type; (d) numerical scheme.

Table 1 .
Summary and comparison of the advantages and shortcomings of 3D and 2D models.

Table 1 .
Summary and comparison of the advantages and shortcomings of 3D and 2D models.

Table 2 .
Overview of studies on 3D hydrodynamic modelling of large-scale dam-break flooding over real-world topography.
Status of the CFD model.This can be commercial, freeware, open-source, or research.Water 2023, 15, 3130