Dam-break Problem Research Articles

An immersed multi-material arbitrary Lagrangian–Eulerian finite element method for fluid–structure-interaction problems

Fluid–structure-interaction (FSI) phenomena are widely concerned in engineering practice and challenge current numerical methods. In this article, the finite element method is strongly coupled with the multi-material arbitrary Lagrangian–Eulerian (MMALE) method to develop a monolithic FSI method named the immersed multi-material arbitrary Lagrangian–Eulerian finite element method (IALEFEM). By immersing the finite elements in the MMALE computational grid, the fluid–solid interface is directly tracked by the element boundary with accurate normal directions. The fluid–structure-interaction is implicitly implemented by assembling the nodal variables and updating the Lagrangian momentum equation on the MMALE grid. Combining the advantages of both MMALE and FEM with the immersed boundary method, the IALEFEM is effective for solving complicated FSI problems with multi-material fluid flow. A slip fluid–structure-interaction method is also proposed to enhance the computational accuracy in simulating FSI problems with significantly different velocity fields. The accuracy and effectiveness of the IALEFEM are verified and validated by several benchmark numerical examples including the shock-cylinder obstacle interaction, flexible panel deformation induced by shock wave, dam break problem with large structural deformation, water entry of a wedge, fragmentation of a cylinder shell induced by blast, response of elastic plate subjected to spherical near-field explosion and structural damage of open-frame building under blast loading.

Modeling fast flows with variable water content: A depth-integrated SPH approach

Water content is one important factor on which velocities, heights, and runout of debris flows and similar phenomena depend. To this purpose, we need two ingredients (i) a mathematical model describing the incorporation of water into the moving soil, which results in a change of water content, and (ii) a rheological model with properties depending on the water content. Modeling of such problems can be done either by using either a: (i) two phases approach, where velocities of solid and water may be different, using two sets of nodes, or (ii) two phases approach where velocities of both are assumed to be the same, using a single set of nodes. In both cases, the models have to implement a mechanism for the water inflow -or outflow-. We will modify both types of two phases models (one or two sets of nodes for solid and water) to include the change of water content due to water inflow. Implementation in the SPH requires extending the algorithm and updating the smoothing length because it is based on the mass of particles and their relative position. Updating the smoothing length when only changes mass is to be avoided. Regarding the rheological model, we will introduce a new model for frictional debris flows implementing a Voellmy coefficient which depends on water content. Alternatively, we will propose a more consistent model based on Bagnold’s idea of introducing a 1D concentration parameter (λ). Finally, we will illustrate the proposed model capability with two examples, a dam break problem, and a real case in El Salvador where the water content played an important role in the propagation properties of a debris flow.

Advances of the in-house developed SWLBM framework in simulating large-scale three-dimensional violent free surface flow with intense splashing

The accurate and efficient simulation for violent free surface flow with intense splashing is import in engineering. The purpose of this paper was to extend and validate the capabilities of Sunway Lattice Boltzmann Method code (SWLBM, our in-house developed CFD framework) in simulating large-scale three-dimensional violent free surface flow. The lattice Boltzmann method was employed to solve the fluid dynamics. The interface was captured by the single-phase free surface model. For parallel computing, the computational domain was divided into parallel blocks and overlap layers were designed for inter-block communications. Several typical dam-break problems were selected for validating the ability of reproducing splashing details, where finest spatial resolution was up to about 0.6 billion cells. The numerical results were in good agreement with experimental results. The present results revealed more plentiful splashing details than various published results with relatively coarser spatial resolution. The efficiency of SWLBM was over 100 times higher than that of OpenFOAM in the testing example. It was demonstrated that SWLBM is capable of simulating large-scale violent free surface flow and reproducing splashing details with sufficient accuracy and efficiency. SWLBM has the potential to be applied in real engineering problems including simulating wave impact on decks.

New optical hydrodynamic representation of dispersive two-phase

In this paper, we construct the photonic dam-break flow problem for [Formula: see text] magnetic fluid in a spherical model. Then, we obtain an optical magnetic transform for the NLSE in hydrodynamical form. By dispersive photonic hydrodynamic representation, normal of surface [Formula: see text] flow is obtained. Thus, we design two-phase [Formula: see text] flow dispersion density in a spherical model. Finally, we have new modeling of dispersive dam break two-phase [Formula: see text] flux.

Well-Balanced conservative central upwind scheme for solving the dam-break flow problem over erodible bed

This work deals with the numerical solution of dam-break flow over an erodible bed. The mathematical model is a combination of the shallow water, the transport diffusion and the bed morphology change equations. The system is solved by a well-Balanced central upwind scheme with conservative property. Several tests are illustrated in order to validate the accuracy and the performance of the model. A comparison of central upwind scheme and Roe scheme is presented.

Increasing flood awareness through dam-break serious games

Dams are one of the most important human-made structures ever conceptualized and allow the development of society by providing multiple uses, such as the development of hydroelectric plants and as a source of water supply. A dam break problem is a catastrophic event that evolves rapidly, causing uncontrollable large floods downstream. In this paper, we develop a simplified modeling approach to assess flood characteristics associated with dam-break problems. The method offers a useful tool to improve the perception of dam safety in terms of the hydrodynamic impacts associated with a dam break. We apply our framework to 20 dams in Brazil, in addition to the Brumadinho dam failure at Córrego do Feijão. This event occurred in Brazil in 2019 leading to almost 300 fatalities. The second case study demonstrates the use of the modeling framework developed in this paper through the simulation of 20 dams in Brazil. The modeling approach uses GIS databases, Google Earth, and National Water Agency (ANA) databases and can be replicated whenever GIS information on dam characteristics, downstream channel, and downstream community is available. The results of this modeling approach indicate that several dams in the northeast of Brazil have relatively large flood hazards. A simplified dam-break hazard index was developed to establish a relative hazard impact that considers only deterministic factors such as the hydrodynamic force, velocity, and depth, as well as the arrival time of the maximum values of these states. These values are determined by a 1-D full momentum solver model (HydroHP-1D).

A Comprehensive Numerical Overview of the Performance of Godunov Solutions Using Roe and Rusanov Schemes Applied to Dam-Break Flow

As open channel simulations are of great economic and human significance, many numerical approaches have been developed, with the Godunov schemes showing particular promise. To evaluate, confirm, and extend the simulation results of others, a variety of first- and second-order FVMs are available, with Rusanov and Roe schemes being used here to simulate the demanding case of 1D and 2D flows following a dam break. The virtual boundary cells approach is shown to achieve a monotonic solution for both interior and boundary cells, and while flux computation is employed at boundary cells, a refinement is only rarely used in existing models. A number of variations are explored, including the TVD MUSCL-Hancock (monotone upwind scheme for conservation laws) numerical scheme with several slope limiters in a quest to avoid spurious oscillations. The sensitivity of the results to both channel length and the ratio of downstream to initial upstream water depth is explored using 1D and 2D models. The Roe scheme with a Van Leer limiter as a slope limiter is shown to be both fast and slightly more accurate than other slope limiters for this problem, but the Rusanov scheme with different slope limiters works well for 1D simulations. Significantly, the selection of an appropriate slope limiter is shown to be best based on the ratio of the downstream to upstream water depth. However, this study focuses on the special case where the ratio of the initial depth downstream to upstream of the dam is equal to or less than 0.5, and these outcomes are compared to theoretical results. The 2D dam-break problem is used to further explore first- and second-order methods using different slope limiters, and the results show that the Superbee limiter can be problematic due to an observed large dispersion in depth contours. However, the most promising approaches from previous studies are confirmed to deserve the high regard given to them by many researchers.

Evolution of dispersive shock waves to the complex modified Korteweg–de Vries equation with higher-order effects

In this paper, new dispersive shock waves (DSWs) in step-like initial value problems to the complex modified Korteweg–de Vries (cmKdV) equation with higher-order effects are found via Whitham modulation theory. For the aforementioned equation, the 1-genus and 2-genus periodic solutions and the associated Whitham equations which are used to describe DSWs are firstly given by the finite-gap integration method, and we also analyze nine types of rarefaction waves appearing before DSWs under the 0-genus Whitham equations. Subsequently, the DSW solutions with step-like initial data are discussed, where we acquire some DSW structures that have not been previously proposed. These notable new results include 1-genus DSW satisfying that one Riemann invariant is constant and the other three are variables and 2-genus DSW in the DSW solutions with one step-like initial data, as well as 3-genus DSW resulting from the collision to 1-genus and 2-genus or two 2-genus DSWs propagating toward each other in the possible DSW solutions with two step-like initial data. Ultimately, the dam break problem is explored to demonstrate the significant physical application of the theoretical findings.

Comparative study of WCSPH, EISPH and explicit incompressible-compressible SPH (EICSPH) for multi-phase flow with high density difference

This study presents three Smoothed Particle Hydrodynamics (SPH) methods capable of handling high-density differences in violent incompressible multiphase flows. The conventional Weakly Compressible SPH (WCSPH) is reformulated into a quasi-Lagrangian framework based on Arbitrary Lagrangian–Eulerian (ALE) context. The Explicit Incompressible SPH (EISPH) method is extended to handle multiphase flows and reformulated in the ALE framework. The Explicit Incompressible-Compressible SPH (EICSPH) method, which can handle both compressible and incompressible phases, is developed by combining these two approaches in a fully explicit algorithm. The proposed methods are validated and compared through four benchmark problems including Rayleigh-Taylor instability, hydrostatic, liquid sloshing and dam break problems. Firstly, the stability and accuracy of interface modeling of the three methods were verified through Rayleigh-Taylor instability with small density differences. In the hydrostatic problem with a large density difference, the results from all three methods exhibit good agreement in the pressure distribution. Particularly, EICSPH demonstrates the faster convergence when compared to WCSPH, with EISPH showing fastest convergence overall. In the transient sloshing problem, all three methods quantitatively converged to the experimental results and exhibited good agreement, although slight pressure noise was observed in WCSPH initially. Finally, in the dam break problem, all three methods successfully simulated sharp interfaces without non-physical voids. The temporal variations of pressure and height were well predicted by all three methods, with EISPH showing better conformity to the water-air interface morphology obtained from other incompressible numerical methods compared to WCSPH and EICSPH. Additionally, the impact of air speed of sound was examined in EICSPH, where while the difference in pressure variation at the probe was minimal, differences were observed in energy dissipation and the progression of the free surface due to the air cushion effect.

Whitham modulation theory and dam-breaking problem under periodic solutions to the defocusing Hirota equation

Whitham modulation theory and dam-breaking problem under periodic solutions to the defocusing Hirota equation

Whitham modulation theory and dam-breaking problem under periodic solutions to the defocusing Hirota equation

Для дефокусирующего уравнения Хироты, которое описывает распространение ультракоротких импульсов в оптических волокнах с дисперсией третьего порядка и эффектами самоусиления высшего порядка, изучаются модуляционная теория Уизема и одно из ее физических приложений - задача о разрушении плотины. Для получения решений используется подход конечнозонного интегрирования. Найдены периодические решения и обсуждается вырождение периодического решения рода один в солитонное решение. Кроме того, получены соответствующие уравнения Уизема для римановых инвариантов, которые можно использовать для модуляции периодических решений при ступенчатых начальных данных. Эти уравнения в пределе малой дисперсии представляют собой квазилинейные гиперболические уравнения и описывают усредненную динамику быстрых колебаний, называемых дисперсионными ударными волнами, которые возникают как решения дефокусирующего уравнения Хироты. Рассмотрен случай, когда характеристические скорости в уравнениях Уизема рода ноль равны нулю, а в качестве критических принимаются значения двух полученных римановых инвариантов. С использованием этих значений как ступенчатых исходных данных найдены и исследованы решения уравнений Уизема для волн разрежения и дисперсионных ударных волн. Для специальных ступенчатых начальных данных исследована точка, в которой в определенный момент времени сталкиваются две дисперсионные ударные волны рода один, т. е. точка, где возникает дисперсионная ударная волна рода два. Наконец, как важное физическое приложение модуляционной теории Уизема обсуждается задача о разрушении плотины.

Методы расчета растекания опасных и загрязняющих веществ по рельефу

The study considers and compares several methods of calculation of the process of stable liquid spread over a solid impermeable surface: the SPH method and the VOF method for the three-dimensional system of equations; the Lax-Wendroff method and the finite volume method for the two-dimensional «shallow water» system of equations. The «shallow water» systems of equations are obtained by averaging the full system of equations over depth assuming the absence of a vertical velocity component. The procedure of numerical calculation by the Lax-Wendroff method is provided in detail. The emphasis is made on considering shallow water approximation as such approximation enables obtaining a three-dimensional flow pattern in the framework of a two-dimensional model. The «shallow water» system of equations is provided taking into account the action of friction forces. All four calculation methods have been verified by using the data of a water dam breaking experiment in a 122-meter canal. The experiments recorded the dynamics of liquid propagation and water rise at different locations and moments. The comparison implies that the SPH method requires significant computational costs due to the need to specify a large number of particles in order to ensure acceptable accuracy. The VOF calculation method blurs the air-water interface, which hampers the determination of spill configuration and the free surface position. The dam breaking problem has been solved most accurately by two methods, namely the Lax-Wendroff method and the finite volume method, which has been confirmed by the quantitative assessment of error in calculations by various methods. It has been demonstrated that the shallow water approximation implemented by the Lax-Wendroff numerical method used in the study ensures accuracy sufficient to solve problems of spill over the terrain surface.

Equipment Safety in Renewable Energies Exploitation

This paper considers the dam-break problem in a horizontal smooth 1D channel, for the purpose of equipment safety in renewable energies exploitation. The fluid is water and it can be described by a Newtonian model, provided that the inertial effects be neglected versus the viscous ones in the momentum balance. Assuming the shallow water approximation, a non dimensional equation is built from the continuity and the Navier-Stokes equations in the limit of zero-inertia and it is solved analytically in two limits: short time and long time. These solutions are then combined into a single, universal model. Limitations of the model are examined by comparison to a converged finite difference numerical solution of the flow equation.

Multiscale air entrainment in wave-in-deck loads

Since entrapped air directly affects the properties of wave impact loads, it has long been unclear whether an air cushioning or entrapped-air amplifying effect exists. Wave-in-deck impacts are innovatively divided into four types based on the air-entrapped scale and characteristics of loads, namely, direct impacts, wave impacts with large or small air pockets (several metres to dozens of metres), and wave impacts with minute bubble plumes (tens of microns to several millimetres). In this study, a systematic study of multiscale air entrapment when waves impact a flat deck is conducted. After volume averaging, the temporal and spatial closure terms are rationally modelled to develop a multiscale air-entrapped wave impact model that couples the compression and expansion properties of large air pockets with the mean hydrodynamic properties of unsteady, nonuniform bubble plumes at a single acceptable grid scale. The high aeration and disordered bubble plume field, which the model successfully captured, as well as the impulsive pressure, have been validated for the typical dam-break impact problem. The results demonstrate that the model is capable of simulating air cavities entrapped in the initial moment of wave impact on the deck and the minute bubble plumes formed by the subsequent breakup, which offers a plausible new explanation for the investigation of the complicated mechanism of multiscale air-entrapped impact.

A stable scheme of the Curvilinear Shallow Water Equations with no-penetration and far-field boundary conditions

This paper presents a stable and highly accurate numerical tool for computing river flows in urban areas, which is a first step towards a numerical tool for flood predictions. We start with the (linearized) well-posedness analysis by Ghader and Nordström (2014), where far-field boundary conditions were proposed and extend their analysis to include wall boundaries. Specifically, we employed high-order Summation-by-parts (SBP) finite-difference operators to construct a scheme for the Shallow Water Equations. We also developed a stable SBP scheme with Simultaneous Approximation Terms that impose far-field and wall boundaries. Finally, we extended the schemes and their stability proofs to non-Cartesian domains. To demonstrate the strength of the schemes, we performed computations for problems with exact solutions to obtain second, third, and fourth (2, 3, 4) convergence rates. Finally, we applied the 4th-order scheme to steady river channels, the canal (or flood-control channel simulations), and dam-break problems. The results show that the imposition of the boundary conditions is stable, and the far-field boundaries cause no visible reflections at the boundaries.

Deep convolutional architectures for extrapolative forecasts in time-dependent flow problems

Physical systems whose dynamics are governed by partial differential equations (PDEs) find numerous applications in science and engineering. The process of obtaining the solution from such PDEs may be computationally expensive for large-scale and parameterized problems. In this work, deep learning techniques developed especially for time-series forecasts, such as LSTM and TCN, or for spatial-feature extraction such as CNN, are employed to model the system dynamics for advection-dominated problems. This paper proposes a Convolutional Autoencoder(CAE) model for compression and a CNN future-step predictor for forecasting. These models take as input a sequence of high-fidelity vector solutions for consecutive time steps obtained from the PDEs and forecast the solutions for the subsequent time steps using auto-regression; thereby reducing the computation time and power needed to obtain such high-fidelity solutions. Non-intrusive reduced-order modeling techniques such as deep auto-encoder networks are utilized to compress the high-fidelity snapshots before feeding them as input to the forecasting models in order to reduce the complexity and the required computations in the online and offline stages. The models are tested on numerical benchmarks (1D Burgers’ equation and Stoker’s dam-break problem) to assess the long-term prediction accuracy, even outside the training domain (i.e. extrapolation). The most accurate model is then used to model a hypothetical dam break in a river with complex 2D bathymetry. The proposed CNN future-step predictor revealed much more accurate forecasting than LSTM and TCN in the considered spatiotemporal problems.

A Finite Volume Method for a 2D Dam-Break Simulation on a Wet Bed Using a Modified HLLC Scheme

This study proposes a numerical model for depth-averaged Reynolds equations (shallow-water equations) to investigate a dam-break problem, based upon a two-dimensional (2D) second-order upwind cell-centre finite volume method. The transportation terms were modelled using a modified approximate HLLC Riemann solver with the first-order accuracy. The proposed 2D model was assessed and validated through experimental data and analytical solutions for several dam-break cases on a wet and dry bed. The results showed that the error values of the model are lower than those of existing numerical methods at different points. Our findings also revealed that the dimensionless error parameters decrease as the wave propagates downstream. In general, the new model can model the dam-break problem and captures the shock wave superbly.

Mathematical and numerical modelling of rapid transients at partially lifted sluice gates

In the present paper, we study the mathematical and numerical modelling of rapid transients at partially lifted sluice gates in the context of one-dimensional Shallow water Equations. First, improved exact solutions of the dam-break problem with partially lifted gate are presented, assuming (i) the dependence of the gate contraction coefficient on the upstream flow depth, and (ii) a viable definition of the submerged flow equation. We show that an exact dam-break solution always exists for any set of initial conditions, but there are also initial conditions for which the solution is multiple. To cope with this case, a novel disambiguation criterion based on the continuous dependence of the solution on the initial conditions is used to select the physically congruent choice amongst the alternatives. Finally, we present a one-dimensional Finite Volume numerical model for the approximate solution of the Shallow water Equations equipped with an approximate Riemann solver for the sluice gate treatment at cells interfaces. The numerical experiments show that the embedding of the steady state gate equations (equilibrium approach) into the approximate Riemann solver leads to unsatisfactory dam-break simulations, while a novel relaxed version of the gate equations (non-equilibrium approach) supplies results that are in agreement with both the novel exact solutions and the laboratory dam-break results available from the literature.

Numerical study of the dam-break flood over natural rivers with macroscopic rocks on movable beds

This paper presents a three-dimensional model of dam break flows over fixed and movable beds. As the consequences of a dam break, the model considers the transport of solid particles and deposition due to the momentum of the flow. The movement of the free surface of water and mud is performed by Newtonian and non-Newtonian fluid models, and the solid macroscopic particles movement is carried out by the discrete phase model (DPM) and macroscopic particle model (MPM) models. It has been detected that the model was reliable and well balanced, and could accurately capture the dam break flow movement in complex terrain. Moreover, using the proposed model, a partial dam break of the Mynzhylky Dam was simulated. Even more in the calculation, the presence of mud sediment and solid particles were taken into account, which is very close to the real dam break problem.

Numerical investigations of dam-break flow impacting on an elastic beam using various FSI coupling algorithms

The occurrence of green water and slamming in severe sea conditions can often be simplified as a dam-break problem. The flow characteristics of dam-break are similar with those on a ship’s deck and can result in structural damage. In this study, the fluid-structure interaction (FSI) of dam-break flow impacting on an elastic beam is investigated based on CFD-FEM method. The FSI coupling is solved in a partitioned manner. The fluid field is solved by OpenFOAM and the structure is calculated by self-developed code using FEM. The two-way coupling algorithm has been implemented to update the mesh of the fluid field. An investigation on mesh independence and the comparison of results with other methods have been conducted to validate the simulation results. After that, three types of FSI coupling algorithms have been utilized to examine the impact on both computational accuracy and efficiency. It is studied that the computational accuracy of all three FSI coupling algorithms is in good agreement. The FSI coupling algorithm utilizing weak iteration exhibits excellent performance in terms of both computational accuracy and efficiency. For the strong coupling algorithm, it is crucial to make a rational selection of the outer and inner iteration numbers in PIMPLE loops.