A two-dimensional dam-break flood plain model

Hromadka, T.V.; Berenbrock, Charles; Freckleton, J.R.; Guymon, Gary L.

doi:10.1016/0309-1708(85)90074-0

Cited by 53 publications

(25 citation statements)

References 2 publications

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“…Finite difference schemes and finite element techniques have been implemented to approximate the solution of the DSW equation and have been used successfully to simulate water flow in shallow systems in [5,14,15,19,32,36,37]. However, no formal mathematical analysis has been carried out in order to show, for example, that the proposed methods converge in some sense to the true solution of the IBVP (Eq.…”

Section: Literature Reviewmentioning

confidence: 98%

“…Diverse numerical schemes have been implemented to approximately solve the DSW equation appearing in the IBVP (Eq. 1) and have been successfully applied as suitable models to simulate overland flow and water flow in vegetated areas such as wetlands [14,15,19,36,37]; yet, no formal mathematical analysis has been carried out in order to study the properties of approximate solutions such as well posedness of the discrete problem, error estimates between the true solution (if uniqueness holds) and the numerical approximant, rates of convergence, and so on. This paper is an initial step in that direction.…”

Section: Introductionmentioning

confidence: 99%

“…These conditions allow the use of scaling arguments to approximate the shallow water system of equations (SWE) by a single doubly nonlinear and degenerate diffusion equation, the DSW equation. Solving the DSW equation computationally requires significantly less work than solving the SWE [19]; thus, it is relevant to explore its applicability and mathematical properties.…”

Section: Introductionmentioning

confidence: 99%

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A numerical approach to study the properties of solutions of the diffusive wave approximation of the shallow water equations

Santillana

Dawson

2009

Comput Geosci

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In this paper, we study the properties of approximate solutions to a doubly nonlinear and degenerate diffusion equation, known in the literature as the diffusive wave approximation of the shallow water equations (DSW), using a numerical approach based on the Galerkin finite element method. This equation arises in shallow water flow models when special assumptions are used to simplify the shallow water equations and contains as particular cases the porous medium equation and the p-Laplacian. Diverse numerical schemes have been implemented to approximately solve the DSW equation and have been successfully applied as suitable models to simulate overland flow and water flow in vegetated areas such as wetlands; yet, no formal mathematical analysis has been carried out in order to study the properties of approximate solutions. In this study, we propose a numerical approach as a means to understand some properties of solutions to the DSW equation and, thus, to provide conditions for which the use of the DSW equation may be inappropriate from both the physical and the mathematical points of view, within the context of shallow water modeling. For analysis purposes, we propose a numerical method based on the Galerkin method and we obtain a priori error estimates between the approximate solutions and weak solutions to the DSW equation under physically consistent assumptions. We also present some numerical experiments that provide relevant information about the accuracy of the proposed numerical method to solve the DSW equation and the applicability of the DSW equation as a model to simulate observed quantities in an experimental setting.

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Section: Literature Reviewmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A numerical approach to study the properties of solutions of the diffusive wave approximation of the shallow water equations

Santillana

Dawson

2009

Comput Geosci

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“…The obtained results show that shallow water scheme is reasonably suitable for the representation of free surface sharp transient (Wang et al, 2000) and the authors concluded that shallow water methods agree satisfactorily with experimental results (Alcrudo, 1998). Other examples of successful representation of dam-break flows with the shallow water approach are available in literature (Xanthopoulos et al, 1976;Hromadka et al, 1985;Fraccarollo and Toro, 1995;Aricò et al, 2007).…”

Section: Introductionmentioning

confidence: 99%

CFD modelling approach for dam break flow studies

Biscarini

Francesco

Manciola

2010

Hydrol. Earth Syst. Sci.

136

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Abstract. This paper presents numerical simulations of free surface flows induced by a dam break comparing the shallow water approach to fully three-dimensional simulations. The latter are based on the solution of the complete set of Reynolds-Averaged Navier-Stokes (RANS) equations coupled to the Volume of Fluid (VOF) method.The methods assessment and comparison are carried out on a dam break over a flat bed without friction, a dam break over a triangular bottom sill and a dam break flow over a 90 • bend. Experimental and numerical literature data are compared to present results.The results demonstrate that the shallow water approach, even if able to sufficiently reproduce the main aspects of the fluid flows, loses some three-dimensional phenomena, due to the incorrect shallow water idealization that neglects the three-dimensional aspects related to the gravity force.

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“…By comparing the results with the analytical solutions, the study rated the performance of the model to be poor. In another study, Hromadka [14] analyzes a two-dimensional dam-break model developed for a flood plain, with flow equations solving a diffusion model coupled to the equation of continuity. The study concludes this approach can better predict at a two-dimensional dam-break flood plain over a broad, flat plain more accurately than a one-dimensional model.…”

Section: History Of Ross Barnett Reservoir Dammentioning

confidence: 99%

Potential Impact of Climate Changes on the Inundation Risk Levels in a Dam Break Scenario

Yerramilli

2013

IJGI

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Abstract:The overall objective of the study is to generate information for an enhanced land use planning with respect to flood hazards. The study assesses the potential impact of climate change by simulating a dam break scenario in a high intensity rainfall event and evaluates the vulnerability risk in the downstream region by integrating ArcGIS and Hydrologic Engineering Centers River Analysis System (HEC-RAS) technologies. In the past century, the evidence of climate changes are observed in terms of increase in high intensity rainfall events. These events are of high concern, as increased inflow rates may increase the probability of a dam failure, leading to higher magnitude flooding events involving multiple consequences. The 100 year historical rainfall data for the central Mississippi region reveals an increased trend in the intensity of rainfall rates after the 1970s. With more than 10% of high hazard dams in the central region, the damage can be far accumulative. The study determines occurrence of the high intensity rainfall event in the past 100 years for central Mississippi and simulates a Ross Barnett Reservoir dam break scenario and evaluates the vulnerability risks due to inundation in the immediate downstream region, which happens to be the State Capital. The results indicate that the inundation due to a Ross Barnett Reservoir failure under high intensity rainfall event is comparable to a catastrophic flood event experienced by the region in 1979, which almost equals a 200-year flood magnitude. The results indicate that the extent and depth of flood waters poses a significant destructive threat to the state capital, inundating various infrastructural and transportation networks.

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A two-dimensional dam-break flood plain model

Cited by 53 publications

References 2 publications

A numerical approach to study the properties of solutions of the diffusive wave approximation of the shallow water equations

A numerical approach to study the properties of solutions of the diffusive wave approximation of the shallow water equations

CFD modelling approach for dam break flow studies

Potential Impact of Climate Changes on the Inundation Risk Levels in a Dam Break Scenario

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