Two-dimensional Dam-break Flow Research Articles

Numerical modeling of liquid spills from the damaged container and collision of two rising bubbles in partially filled enclosure using modified Volume-Of-Fluid (VOF) method

In the present work, two crucial shortcomings associated with Volume-Of-Fluid (VOF) model namely: (1) spurious interface smearing arising from false-diffusion errors, and (2) non-physical velocity fluctuation across the physical discontinuities, are systematically addressed, aiming to establish a unique methodological foundation and guidelines for the enhancement of interface-capturing techniques in handling multi-fluid flows. To accomplish this objective, first, a novel third-order bounded convection scheme is derived based on the Normalized Variable Diagram and Total Variation Diminishing concepts (NVD-TVD) and is then applied for the discretization of the volume-fraction equation. To cope with the instability issue induced by pressure fluctuation, the standard version of the implicit non-iterative PISO algorithm is first modified by incorporating the third pressure-correction step into the algorithm and is then utilized for the treatment of the pressure-velocity coupling. A feasibility and applicability of the proposed modifications in dealing with violent free-surface and multi-fluid flows are demonstrated against the five different challenging benchmark cases including two-dimensional dam-break flow over the dry bed, oil spill from the damaged container, single bubble rising, merging of two rising bubbles and two-fluid Rayleigh-Taylor Instability problems. The comparison of the obtained results with previously published literatures vividly corroborates the robustness and versatility of the modified VOF model in handling multi-fluid flows involving interface coalescence and breakup events. In the last staged, three new benchmark solutions namely (1) coalescence of two consecutive bubbles inside the partially filled enclosure, (2) two-dimensional three-fluid Rayleigh-Taylor Instability, and (3) oil/water spilling from the damaged tank are analyzed using the verified VOF method, aiming to provide a high-quality validation data for CFD simulations.

Initial stages of a three dimensional dam break flow

Short time behavior of a three dimensional, gravity-driven free surface flow is studied analytically and numerically. Initially the fluid is at rest, held by a vertical wall. A rectangular section of the wall suddenly disappears and the gravity driven three-dimensional flow starts. In order to describe the flow in the early stage, the potential theory is employed. Viscous effects are ignored for small times. The leading order problem is solved by using the Fourier series method and an integral equation method. Local analysis of the flow field close to the side edges of the rectangular section reveals a square root singularity. The flow velocity is also log-singular at the bottom edge of the rectangular section. In the limiting case, as the width of the rectangular section approaches infinity, the results of the classical two-dimensional dam break flow are recovered. Three dimensional effects become important closer to the side edges of the rectangular section.

An enhanced CLSVOF method with an algebraic second-reconstruction step for simulating incompressible two-phase flows

The CLSVOF (coupled level set method and volume of fluid) method is a widely-used approach for capturing interfaces in engineering applications of computational fluid dynamics (CFD) due to its accurate interface computation, small mass error and ease of extension to 3D (three-dimensional) simulations. To further enhance this method, a second-reconstruction CLSVOF method is used to simulate incompressible two-phase flows issues with high surface tension effects or not. In the proposed improved method, an algebraic second-reconstruction step is introduced and will be performed after the re-initialization step of the standard CLSVOF process, aiming at obtaining accurate two-phase flow interface parameters. The proposed method introduces a new interface function by means of a sigmoid formula, based on the ultimate LS function calculated by the standard CLSVOF steps. In order to evaluate the superiority of the proposed method compared to existing methods, several benchmark tests are carried out, including two-dimensional rising bubble, three-dimensional rising bubble, two-dimensional dam-break flow with a wet bed, and three-dimensional dam-break flow with an obstacle. The results show that the proposed method is more accurate than existing methods, while guaranteeing almost no mass error. In addition, the simulated results of the air-water interface agree well with those in previous experiments data.

Experimental study of bed morphology evolution under two-dimensional dam-break flow

The present study discusses the evolution of bed morphology under 2D dam-break flow by conducting a set of laboratory experiments. The experiments were conducted in a 1.6 m × 28 m × 1.0 m glass flume with non-uniform fly ash as the bed material. Two scenarios were designed: no inflow (scenario 1) and nearly constant water level (scenario 2) in the upstream reservoir. During the experiment, the water levels were measured by pressure sensors which were buried under the sediment layer, and the bed morphology was measured by an ultrasonic ranging system. The results showed that: (1) in scenario 1, the range and depth of the scour pit continued to increase, but the location of the deepest scour point did not change significantly; (2) in scenario 2, the depth and range of scour increased after the dam break, but the growth rate slowed down obviously after t = 15 min. The data can be employed to understand the bed morphology evolution under a dam-break flow, validate numerical approaches, and test geomorphic flood models.

Multiphase smoothed particle hydrodynamics modeling of diffusive flow through porous media

This paper presents a numerical model using smoothed particle hydrodynamics for simulating diffusive flow in porous media with spatially varying porosity, especially when high permeability permits fast flow. The governing equations are based on a two-phase mixture theory that describes porosity in terms of stationary solid particles carrying information about volume fraction. The diffusion equation is first validated by application to two-dimensional diffusion within a square box. The continuity and momentum equations taking account of porosity are then validated by simulating Darcy seepage flow in a U-tube filled with a porous medium. Good agreement between numerical results and predicted data is obtained, demonstrating the validity of the multiphase model. Finally, the model is applied to diffusion in a two-dimensional dam-break flow through a porous structure.

A high-efficiency smoothed particle hydrodynamics model with multi-cell linked list and adaptive particle refinement for two-phase flows

The smoothed particle hydrodynamics method has been applied in modeling violent flows with the free surface. Much effort has been made in reducing the computational costs in simulating the three-dimensional two-phase flows with the violently deformed free surface and breaking waves. Although the adaptive particle refinement approach has been developed to concentrate fine resolution only in the region of interest, its efficiency still hardly meets the demand of large-scale numerical simulation. In order to improve its efficiency further, a multi-cell linked list algorithm coupling with the adaptive particle refinement for the smoothed particle hydrodynamics model is implemented in the graphic processing unit-based code. Particles are identified not only by its position but also by its resolution and trait. The accuracy of the numerical model for solving two-phase flows with the free surface is validated through computing a two-dimensional dam-break flow and the hydrodynamic flows of spheres vertically entering the water from the air. The numerical results agree well with the experimental data available. For the cases of water entry of a sphere of different densities, the development of open cavity and cavity sealing is discussed in terms of the pinch-off depth and the corresponding sphere depth. Simulations show that the smoothed particle hydrodynamics method with the adaptive particle refinement possesses the characteristics of good accuracy, time-saving, and high efficiency in simulating three-dimensional two-phase flows.

Comparison of Taylor Galerkin and FTCS models for dam-break simulation

The aim of this paper is to compare the ability of two numerical models to simulate two-dimensional dam-break flows. Dam-break modelling is important in reducing the high-risk of dam failure by determining the water flow movement and its effect on buildings downstream. In this study, the Taylor Galerkin and Forward Time Central Space method is presented to simulate 2-D dam-break flow. The Hansen filter is applied to both methods to reduce numerical instability oscillations in the model. The filters were used for each time step at each computing point. The model is verified by comparing the result simulation with numerical results from previous studies. The result show that Taylor Galerkin numerical scheme with Hansen filter is successful to simulate the problem of 2-D dam-break. Also, the Taylor Galerkin model has better results than the FTCS model. Studies like this are needed for mitigation efforts in the event of dam failure.

Smoothed Particle Hydrodynamics Modeling with Advanced Boundary Conditions for Two-Dimensional Dam-Break Floods

To simulate the dynamics of two-dimensional dam-break flow on a dry horizontal bed, we use a smoothed particle hydrodynamics model implementing two advanced boundary treatment techniques: (i) a semi-analytical approach, based on the computation of volume integrals within the truncated portions of the kernel supports at boundaries and (ii) an extension of the ghost-particle boundary method for mobile boundaries, adapted to free-slip conditions. The trends of the free surface along the channel, and of the impact wave pressures on the downstream vertical wall, were first validated against an experimental case study and then compared with other numerical solutions. The two boundary treatment schemes accurately predicted the overall shape of the primary wave front advancing along the dry bed until its impact with the downstream vertical wall. Compared to data from numerical models in the literature, the present results showed a closer fit to an experimental secondary wave, reflected by the downstream wall and characterized by complex vortex structures. The results showed the reliability of both the proposed boundary condition schemes in resolving violent wave breaking and impact events of a practical dam-break application, producing smooth pressure fields and accurately predicting pressure and water level peaks.

SPH study of the evolution of water–water interfaces in dam break flows

The mixing process of upstream and downstream waters in the dam break flow could generate significant ecological impact on the downstream reaches and influence the environmental damages caused by the dam break flood. This is not easily investigated with the analytical and numerical models based on the grid method due to the large deformation of free surface and the water–water interface. In this paper, a weakly compressible smoothed particle hydrodynamics (WCSPH) solver is used to study the advection and mixing process of the water bodies in two-dimensional dam break flows over a wet bed. The numerical results of the mixing dynamics immediately after the release of the dam water are found to agree satisfactorily with the published experimental and numerical results. Then, further investigations are carried out to study the interface development at the later stage of dam break flows in a long channel. The analyses concentrate on the evolution of the interface at different ratios between the upstream and downstream water depths. The potential capabilities of the mesh-free SPH modelling approach for predicting the detailed development of the water–water interfaces are fully demonstrated.

Discussion of “Experimental and Numerical Investigations of Two-Dimensional Dam-Break Flows” by Lindsey Ann LaRocque, Jasim Imran, and M. Hanif Chaudhry

Discussion of “Experimental and Numerical Investigations of Two-Dimensional Dam-Break Flows” by Lindsey Ann LaRocque, Jasim Imran, and M. Hanif Chaudhry

Closure to “Experimental and Numerical Investigations of Two-Dimensional Dam-Break Flows,” by Lindsey Ann LaRocque, Jasim Imran, and M. Hanif Chaudhry

Closure to “Experimental and Numerical Investigations of Two-Dimensional Dam-Break Flows,” by Lindsey Ann LaRocque, Jasim Imran, and M. Hanif Chaudhry

Experimental and Numerical Investigations of Two-Dimensional Dam-Break Flows

This paper presents measurements of velocity profiles obtained from idealized dam-break experiments and results from numerical simulations of these experiments. Dam-break flows were generated in the laboratory by suddenly lifting a gate inside a flume for three different upstream heads with a dry-bed downstream condition. Ultrasonic Doppler velocity profilers were used for recording transient velocity profiles at eight different locations upstream and downstream of the removed gate. These experiments provided data on the spatio-temporal evolution of the flow field in an unsteady flow of relatively short duration. The two-dimensional experiments were simulated using a computational fluid dynamics solver. The following observations are made: (1) turbulence modeling does not affect the velocity profile in the upstream reservoir, but has significant influence on the prediction of downstream velocity; (2) the velocity magnitude at a specific location changes with time, but the shape of the velocity profiles remains similar; (3) an analytical solution for frictionless dam-break flow on a sloping bed and numerical simulation with the large eddy simulation (LES) modeling show satisfactory agreement with measured water surface profile; (4) nondimensionalization of reservoir-side velocity profiles resulting from different reservoir heads and at different locations from a specific head shows excellent collapse and reveals that the shear layer thickness of these profiles is approximately 5% of the initial reservoir head; (5) measurement and simulation with the LES model for turbulence show satisfactory agreement, suggesting that the LES modeling is a viable approach for an accurate prediction of dam-break flows.

Dam-break flows over mobile beds: experiments and benchmark tests for numerical models

In this paper, the results of a benchmark test launched within the framework of the NSF–PIRE project “Modelling of Flood Hazards and Geomorphic Impacts of Levee Breach and Dam Failure” are presented. Experiments of two-dimensional dam-break flows over a sand bed were conducted at Université catholique de Louvain, Belgium. The water level evolution at eight gauging points was measured as well as the final bed topography. Intense scour occurred close to the failed dam, while significant deposition was observed further downstream. From these experiments, a benchmark was proposed to the scientific community, consisting of blind test simulations, that is, without any prior knowledge of the measurements. Twelve different teams of modellers from eight countries participated in the study. Here, the numerical models used in this test are briefly presented. The results are commented upon, in view of evaluating the modelling capabilities and identifying the challenges that may open pathways for further research.

Unsplit 기법을 적용한 흐름율과 생성항의 처리기법

본 연구에서는 마른하도 및 복잡한 지형에서의 파의 전파와 같은 수공학 분야에서 해결하기 어려운 문제를 해석하기 위한 고정확도 2차원 수치모형을 개발하기 위해, unsplit 유한체적기법과 HLLC Riemann 해법을 이용한 흐름율 계산으로 쌍곡선형 적분 보존형의 2차원 천수방정식을 해석하였다. Unsplit 기법의 적용을 위해 하상경사항은 발산정리를 이용하여 이산화한 형태를 적용하였으며, 흐름율과 생성항의 균형을 이루기 위해 수면경사법을 시간과 공간에 대해 2차정확도를 가지는 MUSCL 기법과 연계하였다. 그리고 적용한 생성항 처리기법과 흐름율과의 보존특성이 만족함을 보였다. 2차정확도의 사용으로 불연속 지점에서 발생할 수 있는 수치진동을 제거하기 위해서 경사제한자를 사용한 TVD 기법을 적용하였다. 개발모형을 정확해가 존재하는 생성항이 없는 1차원 댐 붕괴 흐름에 적용하여 흐름율 계산의 정확성을 검증하였고, 하상융기를 가진 하도의 정상류 및 천이류 모의를 통해 개발모형의 보존특성을 검증하였으며, 하상경사 및 단면의 확대/축소구간이 존재하는 2차원 댐 붕괴 흐름에 적용하여 개발모형의 적용성을 검증하였다. The objective of this study is to develop the accurate, robust and high resolution two-dimensional numerical model that solves the computationally difficult hydraulic problems, including the wave front propagation over dry bed and abrupt change in bathymetry. The developed model in this study solves the conservative form of the two-dimensional shallow water equations using an unsplit finite volume scheme and HLLC approximate Riemann solvers to compute the interface fluxes. Bed-slope term is discretized by the divergence theorem in the framework of FVM for application of unsplit scheme. Accurate and stable SGM, in conjunction with the MUSCL which is second-order-accurate both in space and time, is adopted to balance with fluxes and source terms. The exact C-property is shown to be satisfied for balancing the fluxes and the source terms. Since the spurious oscillations in second-order schemes are inherent, an efficient slope limiting technique is used to supply TVD property. The accuracy, conservation property and application of developed model are verified by comparing numerical solution with analytical solution and experimental data through the simulations of one-dimensional dam break flow without bed slope, steady transcritical flow over a hump and two-dimensional dam break flow with a constriction.

Finite Proximate Method for Convection-Diffusion Equation

A finite proximate method was presented to solve the convection-diffusion equation in curvilinear grids. The method has characteristics of automatic upwind effect and the good stability. It was verified through exact solution and other calculation results of two-dimensional dam-break flow in a frictionless, horizontal channel. The calculation results are in good agreement with the exact solution and other calculation results, which show that the finite proximate method can be applied to solve the convection-diffusion equation directly not only in the rectangular grids, but also in the curvilinear grids.

Numerical Simulation of Two-Dimensional Dam-Break Flows in Curved Channels

Two-dimensional transient dam-break flows in a river with bends were theoretically studied. The river was modeled as a curved channel with a constant width and a flat bottom. The water was assumed to be an incompressible and homogeneous fluid. A channel-fitted orthogonal curvilinear coordinate system was established and the corresponding two-dimensional shallow-water equations were derived for this system. The governing equations with well-posed initial and boundary conditions were numerically solved in a rectangular domain by use of the Godunov-type finite-difference scheme, which can capture the hydraulic jump of dam-break flows. The comparison between the obtained numerical results and the experimental data of Miller and Chaudry in a semicircle channel shows the validity of the present numerical scheme. The mathematical model and the numerical method were applied to the dam-break flows in channels with various curvatures. Based on the numerical results, the influence of river curvatures on the dam-break flows was analyzed in details.

Two-dimensional dam break flows of Herschel–Bulkley fluids: The approach to the arrested state

Dam break flows of viscoplastic fluids are studied theoretically using a Herschel–Bulkley constitutive law and a lubrication model of the motion. Following initiation these fluids are gravitationally driven out of the lock in which they had resided. Their motion is eventually arrested because they exhibit a yield stress and they attain a stationary state in which the gravitational forces are in equilibrium with the yield stress. We study the evolution of these flows from initiation to arrest by integrating the equations of motion numerically. We demonstrate that the final arrested state is approached asymptotically and find analytically that the perturbations to the final state decay algebraically with time as 1 / t n , where n is the power index of the Herschel–Bulkley model.

Modelling estuarine and coastal flows using an unstructured triangular finite volume algorithm

Details are given of the development and application of a numerical model for predicting free-surface flows in estuarine and coastal basins using the finite volume method. Both second- and third-order accurate and oscillation free explicit numerical schemes have been used to solve the shallow water equations. The model deploys an unstructured triangular mesh and incorporates two types of mesh layouts, namely the ‘cell centred’ and ‘mesh vertex’ layouts, and provides a powerful mesh generator in which a user can adjust the mesh-size distribution interactively to create a desirable mesh. The quality of mesh has been shown to have a major impact on the overall performance of the numerical model. The model has been applied to simulate two-dimensional dam break flows for which transient water level distributions measured within a laboratory flume were available. In total 12 model runs were undertaken to test the model for various flow conditions. These conditions include: (1) different bed slopes (ranging from zero to 0.8%), (2) different upstream and downstream water level conditions, and (3) initially wet and dry bed conditions, downstream of the dam. Detailed comparisons have been made between model predicted and measured water levels and good agreement achieved between both sets of results. The model was then used to predict water level and velocity distributions in a real estuary, i.e. the Ribble Estuary, where the bed level varies rapidly at certain locations. In order to model the whole estuary, a 1-D numerical model has also been used to model the upper part of the estuary and this model was linked dynamically to the 2-D model. Findings from this application are given in detail.

Central scheme for two-dimensional dam-break flow simulation

A new second-order central scheme (KT), proposed by Kurganov and Tadmor, have been used for the solution of the two-dimensional dam-break problem. After having assumed as basis of the dam-break phenomenon the set of 2D nonhomogeneous Saint–Venant equations, the KT scheme in its semi-discrete second-order form has been extended for taking into account the presence of a source term. Time integration has been performed by using a third-order TVD Runge–Kutta scheme. To demonstrate the accuracy of this explicit method, the solution obtained by this model for a dam-break problem of one-dimensional flow has been compared with the corresponding analytical solution, moreover, the solutions obtained for two test cases of two-dimensional flow have been compared with the experimental results.

Two-dimensional dam break flow simulation

Numerical modelling of shallow water flow in two dimensions is presented in this work with the results obtained in dam break tests. Free surface flow in channels can be described mathematically by the shallow-water system of equations. These equations have been discretized using an approach based on unstructured Delaunay triangles and applied to the simulation of two-dimensional dam break flows. A cell centred finite volume method based on Roe's approximate Riemann solver across the edges of the cells is presented and the results are compared for first- and second-order accuracy. Special treatment of the friction term has been adopted and will be described. The scheme is capable of handling complex flow domains as shown in the simulation corresponding to the test cases proposed, i.e. that of a dam break wave propagating into a 45° bend channel (UCL) and in a channel with a constriction (LNEC-IST). Comparisons of experimental and numerical results are shown.