Dam-break Flow Research Articles

Second-order force scheme for lattice Boltzmann model of shallow water flows

ABSTRACTA force scheme of second-order accuracy in both time and space has been introduced into the lattice Boltzmann model for shallow water equations. The scheme is tested within the single relaxation framework by using a one-dimensional steady flow over a bump, two one-dimensional dam-break flows and a two-dimensional unsteady dam-break flow. It is found that this second-order force scheme can improve the computational accuracy in time compared with the previous force treatment in the lattice Boltzmann model for shallow water. Moreover, the scheme can be also incorporated in the multiple-relaxation-time models.

Ritter’s dry-bed dam-break flows: positive and negative wave dynamics

Dam-break flood waves are associated with major environmental disasters provoked by the sudden release of water stored in reservoirs. Ritter found in 1892 an analytical solution to the wave structure of an ideal fluid released during an instantaneous dam failure, propagating over initially dry horizontal terrain. This solution, though ideal, hence frictionless, is widely used to test numerical solutions of the Shallow Water Equations (SWE), and as educational tool in courses of fluid mechanics, given that it is a peculiar case of the Riemann problem. However, the real wave structure observed experimentally differs in a major portion of the wave profile, including the positive and negative fronts. Given the importance of an accurate prediction of the dam break wave, the positive and negative wave portions originating from the breaking of a dam with initially dry land on the tailwater reach are revisited in this work. First, the propagation features of the dry-front are investigated using an analytical boundary-layer type model (Whitham/Dressler/Chanson model) constructed matching an (outer) inviscid dynamic wave to an (inner) viscous diffusive wave. The analytical solution is evaluated using an accurate numerical solution of the SWE produced using the MUSCL-Hancock finite-volume method, which is tested independently obtaining the solution based on the discontinuous Galerkin finite-element method. The propagation features of the negative wave are poorly reproduced by the SWE during the initial stages of dam break flows, and, thus, are then investigated using the Serre–Green–Naghdi equations for weakly-dispersive fully non-linear water waves, which are solved using a finite volume-finite difference scheme.

A finite volume shock‐capturing solver of the fully coupled shallow water‐sediment equations

SummaryThis paper describes a numerical solver of well‐balanced, 2D depth‐averaged shallow water‐sediment equations. The equations permit variable horizontal fluid density and are designed to model water‐sediment flow over a mobile bed. A Godunov‐type, Harten–Lax–van Leer contact (HLLC) finite volume scheme is used to solve the fully coupled system of hyperbolic conservation laws that describe flow hydrodynamics, suspended sediment transport, bedload transport and bed morphological change. Dependent variables are specially selected to handle the presence of the variable density property in the mathematical formulation. The model is verified against analytical and semi‐analytical solutions for bedload transport and suspended sediment transport, respectively. The well‐balanced property of the equations is verified for a variable‐density dam break flow over discontinuous bathymetry. Simulations of an idealised dam‐break flow over an erodible bed are in excellent agreement with previously published results, validating the ability of the model to capture the complex interaction between rapidly varying flow and an erodible bed and validating the eigenstructure of the system of variable‐density governing equations. Flow hydrodynamics and final bed topography of a laboratory‐based 2D partial dam breach over a mobile bed are satisfactorily reproduced by the numerical model. Comparison of the final bed topographies, computed for two distinct sediment transport methods, highlights the sensitivity of shallow water‐sediment models to the choice of closure relationships. Copyright © 2016 John Wiley & Sons, Ltd.

Coupled incompressible Smoothed Particle Hydrodynamics model for continuum-based modelling sediment transport

A coupled solenoidal Incompressible Smoothed Particle Hydrodynamics (ISPH) model is presented for simulation of sediment displacement in erodible bed. The coupled framework consists of two separate incompressible modules: (a) granular module, (b) fluid module. The granular module considers a friction based rheology model to calculate deviatoric stress components from pressure. The module is validated for Bagnold flow profile and two standardized test cases of sediment avalanching. The fluid module resolves fluid flow inside and outside porous domain. An interaction force pair containing fluid pressure, viscous term and drag force acts as a bridge between two different flow modules. The coupled model is validated against three dambreak flow cases with different initial conditions of movable bed. The simulated results are in good agreement with experimental data. A demonstrative case considering effect of granular column failure under full/partial submergence highlights the capability of the coupled model for application in generalized scenario.

A new coupled level set and volume-of-fluid method to capture free surface on an overset grid system

We present a new coupled level set and volume-of-fluid (CLSVOF) method for free surface flow simulations on an overset grid system. The coupled method takes advantages of the strengths of the level set (LS) method and the volume-of-fluid (VOF) method, and is superior to either single method. The novelty of the present method lies in that we develop the methodology for an overset grid system of embedding, overlapping and moving structured grids. The new methodology accurately captures interface and greatly preserves mass on an overset grid system by demonstrating the 3D sphere advection test. The method is coupled to a well validated Reynolds-Averaged Navier–Stokes incompressible flow solver. The method is validated with the dam-breaking flow interacting with a 3D obstacle (square structure/circular cylinder) by comparing the numerical results with available experimental and numerical studies. The water impact of a sphere case is further performed to demonstrate the capabilities of the new method on a complicated moving overset grid system.

Numerical Simulations of Dam-break Floods with MPM

Due to the ability to model large deformations and the ease of dealing with boundary conditions in a Lagrangian framework, the material point method is getting more popularity in geotechnical engineering applications. In this paper, the material point is tentatively applied to model problems of hydrodynamics as an introduction to this field. Dam-break flows with different initial aspect ratios are simulated in both the material point method and an extensively verified shallow water equations model. In order to test the accuracy and stability of the material point method, simulations of dam-break flows are carried out and the results are in good agreement with other validated numerical methods and experimental data. From the comparisons between the simulations in both the material point method and shallow water equations model, a critical aspect ratio value for the applicability of the shallow water equations is found to be 1. The material point method shows its potential to tackle hydrodynamics related problems.

Impact of Village Resistance Values on Simulating Results of Flood Routing in Floodplains

2-D hydrodynamic model using unstructured triangular meshes was first established. And the model was verified against the analytical solutions and experimental data of dam-break flows in laboratory. Finally, the model was employed to preliminarily simulate inundated floods routing in Lankao and Dongming floodplains of Lower Yellow River (LYR), and the impact of roughness value in village regions on modeling results was thoroughly analyzed. The results show that the water depth for hollowing village region was largest, and the maximum value of water depth increasing was about 0.57 m. Different roughness values in village region had significant impact on flood routing near village. To be specific, the water depth of n = 0.12 was 0.25m larger than that of n = 0.06, the corresponding flow velocity decreased by 0.24 m/s.

Multispeed Lattice Boltzmann Model with Space-Filling Lattice for Transcritical Shallow Water Flows

Inspired by the recent success of applying multispeed lattice Boltzmann models with a non-space-filling lattice for simulating transcritical shallow water flows, the capabilities of their space-filling counterpart are investigated in this work. Firstly, two lattice models with five integer discrete velocities are derived by using the method of matching hydrodynamics moments and then tested with two typical 1D problems including the dam-break flow over flat bed and the steady flow over bump. In simulations, the derived space-filling multispeed models, together with the stream-collision scheme, demonstrate better capability in simulating flows with finite Froude number. However, the performance is worse than the non-space-filling model solved by finite difference scheme. The stream-collision scheme with second-order accuracy may be the reason since a numerical scheme with second-order accuracy is prone to numerical oscillations at discontinuities, which is worthwhile for further study.

Three-dimensional shallow water system: A relaxation approach

We study a three-dimensional shallow water system, which is obtained from the three-dimensional Navier–Stokes equations after Reynolds averaging and under the simplifying hydrostatic pressure assumption. Since the three-dimensional shallow water system is generically not hyperbolic, it cannot be numerically solved using hyperbolic shock capturing schemes. At the same time, existing simple finite-difference and finite-volume methods may fail in simulations of unsteady flows with sharp gradients, such as dam-break and flood flows. To overcome this limitation, we propose a novel numerical method, which is based on a relaxation approach utilized to “hyperbolize” the three-dimensional shallow water system. The extended relaxation system is hyperbolic and we develop a second-order semi-discrete central-upwind scheme for it. The proposed numerical method can preserve “lake at rest” steady states and positivity of water depth over irregular bottom topography. The accuracy, stability and robustness of the developed numerical method is verified on five numerical experiments.

An improved SWE model for simulation of dam-break flows

A finite-difference method based on a shallow water equation (SWE) is developed in this study for simulation of dam-break flows. A second-order leap-frog scheme constructed in a staggered grid system is used to discretise the original SWE. To minimise the spurious fluctuations of the free surface near the moving front, an artificial diffusion term, which is simple, effective and easy to implement in the staggered-grid leap-frog system, is introduced on the right-hand side of the continuity equation. The model is verified against a wide range of classical analytical solutions, experimental data and other previous numerical results. The model is also validated against the real case of the Malpasset dam-break event. It is demonstrated that the improved model is well balanced and robust, and can accurately capture the movement of the dam-break flows.

Analytical solution of dam-break flood wave propagation in a dry sloped channel with an irregular-shaped cross-section

Cross-sectional channel shape is a primary factor influencing dam-break floods. However, it is difficult to analytically understand the impact of the cross-sectional shape on flood wave propagation because most of the existing analytical solutions are only applicable to channels with specific cross-sections (e.g., rectangular, parabolic and triangular cross-sections). Here, a polyline cross-section representing a realistic scenario and derivation method were suggested for analyzing dam-break floods down a dry sloping channel. With the proposed model, the flow depth, average velocity and discharge profiles after an instantaneous dam break can be presented as three dimensionless curves. The effect of bed slope on the dam-break wave was evaluated. Both the flood acceleration on a downward-sloping channel and the flood retardation on an upward-sloping channel are illustrated clearly with the analytical solution in an example application. The effect of the bed slope on wave propagation becomes more prominent over time. The flow depth, average velocity and discharge at the dam site remain constant for a horizontal bed and vary with time for a sloping bed. Three-dimensional numerical simulations of the examples were performed using a large eddy simulation (LES) model along with the Volume of Fluid (VOF) approach for surface tracking. A comparison between the analytical and numerical solutions shows that the analytical model can provide the main features of dam-break floods and therefore can be used for the rapid prediction of dam-break flows. The model limitations are also presented.

A Novel Explicit-Implicit Coupled Solution Method of SWE for Long-term River Meandering Process Induced by Dambreak

Large amount of sediment deposits in the reservoir area can cause dam break, which not only leads to an immeasurable loss to the society, but also the sediments from the reservoir can be transported to generate further problems in the downstream catchment. This study aims to investigate the short-to-long term sediment transport and channel meandering process under such a situation. A coupled explicit-implicit technique based on the Euler-Lagrangian method (ELM) is used to solve the hydrodynamic equations, in which both the small and large time steps are used separately for the fluid and sediment marching. The main feature of the model is the use of the Characteristic-Based Split (CBS) method for the local time step iteration to correct the ELM traced lines. Based on the solved flow field, a standard Total Variation Diminishing (TVD) finite volume scheme is applied to solve the sediment transportation equation. The proposed model is first validated by a benchmark dambreak water flow experiment to validate the efficiency and accuracy of ELM modelling capability. Then an idealized engineering dambreak flow is used to investigate the long-term downstream channel meandering process with non-uniform sediment transport. The results showed that both the hydrodynamic and morphologic features have been well predicted by the proposed coupled model.

Novel Slope Source Term Treatment for Preservation of Quiescent Steady States in Shallow Water Flows

This paper proposes a robust method for modeling shallow-water flows and near shore tsunami propagation, applicable for both simple and complex geometries with uneven beds. The novel aspect of the model includes the introduction of a new method for slope source terms treatment to preserve quiescent equilibrium over uneven topographies, applicable to both structured and unstructured mesh systems with equal accuracy. Our model is based on the Godunov-type finite volume numerical approximation. Second-order spatial and temporal accuracy is achieved through high resolution gradient reconstruction and the predictor-corrector method, respectively. The approximate Riemann solver of Harten, Lax, and van Leer with contact wave restoration (HLLC) is used to compute fluxes. Comparisons of the model’s results with analytical, experimental, and published numerical solutions show that the proposed method is capable of accurately predicting experimental and real-time tsunami propagation/inundation, and dam-break flows over varying topographies.

An improved SPH approach for simulating 3D dam-break flows with breaking waves

In this article, we develop an improved smoothed particle hydrodynamics (SPH) approach for simulating 3D dam-break flows with breaking waves. In order to improve the computational accuracy and pressure distributions, the correction of kernel gradient and the introduction of Rusanov flux into the continuity equation are particularly implemented. Also, both wall and dummy particles are employed for modeling the complex solid boundaries in a flexible way. To show the ability of the improved SPH approach for solving 3D free surface flow problems, three challenging numerical examples including 3D dam-break flow against a vertical wall, against a cuboid obstacle, and against a cylindrical obstacle are numerically simulated and compared with available experimental data in literature. The convergent behavior of the numerical algorithm has also been studied by using different particle resolutions. It is demonstrated that the improved SPH approach is capable of handling with 3D free surface flows with large deformations and fragmentations accurately and stably, and even more important, also computing an accurate and fluctuations-free pressure field.

EFDC 모형을 이용한 댐 붕괴류 수치모의 및 매개변수 민감도 분석

In this study, a series of numerical simulation of dam break flow was conducted using EFDC model, and input conditions including cell size, time step, and turbulent eddy viscosity were considered to analyze parameter sensitivity. In case of coarse mesh layout, the propagated length of the shock wave front was <TEX>${\Delta}_x$</TEX> longer than that of other mesh layouts, and the velocity results showed jagged edge, which can be cured by applying fine grid mesh. Turbulent eddy viscosity influenced magnitude of the maximum velocity passing through gate up to 20% and the cell Peclet number less than 2.0 ensured no numerical oscillations.

A Robust volume conservative divergence-free ISPH framework for free-surface flow problems

This study presents a Volume Conservative approach for resolving volume conservation issue in divergence-free incompressible Smoothed Particle Hydrodynamics (ISPH). Irregular free surface deformation may introduce error in volume computation, which has a cascading effect over time. Proposed correction decreases this numerical compressibility to a minimal value. The correction is obtained directly by solving Navier-Stokes momentum equation. Consequently, the framework does not require any parametric study for mixed source/sink term or iterative solution of pressure Poisson equations. The correction is implemented on four different types of flow: (a) pressurized flow in a closed box, (b) dambreak flow, (c) flow through porous block, (d) lock-exchange flow of immiscible fluids (both free-surface and pressurized flow). All four scenarios are shown to have minimal error compared to pure divergence-free ISPH.

Parallel Computation of a Dam-Break Flow Model Using OpenACC Applications

AbstractTwo key factors in dam-break modeling are accuracy and speed. Therefore, high-performance calculations are of great importance to the simulation of dam-break events. In this study, we develop a two-dimensional hydrodynamic model based on the finite volume method to simulate the dam-break flow routing process. Roe’s approximate Riemann solution is adopted to solve the interface flux of grid cells and accurately simulate the discontinuous flow. A graphics processing unit (GPU)-based parallel method, OpenACC, is used to realize parallel computing. Because an explicit discrete technique is used to solve the governing equations, and there is no correlation between grid calculations in a single time step, the parallel dam-break model can be easily realized by adding OpenACC directives to the loop structure of the grid calculations. To analyze the performance of the model, we considered the Pangtoupao flood storage area in China using a Nvidia Tesla K20c card and four different grid division schemes. By ...

Nonhydrostatic Dam Break Flows. I: Physical Equations and Numerical Schemes

AbstractModeling of dam break flows is frequently required in civil and environmental engineering because of the risk associated with this catastrophic flow. Typically, model predictions are conducted using the Saint-Venant hydrostatic theory, which can lead to unrealistic predictions. The prediction of the amplitude of nonhydrostatic waves generated during dam break flows is an important engineering problem given the risk of overtopping of flow in manmade canals or the increasing of flooding areas in natural watercourses. The weakly nondispersive and fully nonlinear Serre equations are a suitable choice for modeling these flows, but there is a lack of a systematic assessment of this system of equations for dam break flow modeling reported in the literature. In this paper, the Serre equations are applied to dam break flows over horizontal rigid bottoms, whereas in the second part of this research, the nonhydrostatic dam break waves over erodible beds are considered. Here, a high resolution finite volume m...

Nonhydrostatic Dam Break Flows. II: One-Dimensional Depth-Averaged Modeling for Movable Bed Flows

AbstractThe dam break flow over a movable bed is an important problem in fluvial flow processes. These flows are usually predicted by a one-dimensional (1D) approach based on a hydrostatic pressure distribution. Recent three-dimensional (3D) nonhydrostatic simulations of dam break waves over movable beds based on the Reynolds-averaged Navier-Stokes (RANS) equations revealed that the Saint Venant theory is not accurate in predicting the flow dynamics within the scour hole developed. In this work, a generalized 1D nonhydrostatic model for flow over movable beds is proposed assuming a linear, nonhydrostatic, pressure distribution. The new set of 1D equations accounts for the vertical acceleration, which is important in dam break waves over movable beds given the instantaneous curved beds generated over the erodible terrain. These equations account for both the bed and suspended-load transport modes. A high-resolution finite volume numerical scheme with a semi-implicit treatment of nonhydrostatic terms is dev...

Dam break problem for the focusing nonlinear Schrödinger equation and the generation of rogue waves

We propose a novel, analytically tractable, scenario of the rogue wave formation in the framework of the small-dispersion focusing nonlinear Schrödinger (NLS) equation with the initial condition in the form of a rectangular barrier (a ‘box’). We use the Whitham modulation theory combined with the nonlinear steepest descent for the semi-classical inverse scattering transform, to describe the evolution and interaction of two counter-propagating nonlinear wave trains—the dispersive dam break flows—generated in the NLS box problem. We show that the interaction dynamics results in the emergence of modulated large-amplitude quasi-periodic breather lattices whose amplitude profiles are closely approximated by the Akhmediev and Peregrine breathers within certain space-time domain. Our semi-classical analytical results are shown to be in excellent agreement with the results of direct numerical simulations of the small-dispersion focusing NLS equation.