Stability and Accuracy of Weighted Four-Point Implicit Finite Difference Schemes for Open Channel Flow

Venutelli, Maurizio

doi:10.1061/(asce)0733-9429(2002)128:3(281)

Cited by 42 publications

(16 citation statements)

References 4 publications

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“…These oscillatory features in fact signify dramatic numerical oscillations in the ADI code and may be the result of numerical "shocks" being aligned with the topographical grid (e.g. Meselhe and Holly, 1997;Venutelli et al, 2002). In contrast, the TVD data reproduce flow channelisation far more clearly, apparently free of any significant oscillatory behaviour.…”

Section: Hydrodynamic Solver Comparisonmentioning

confidence: 99%

“…Nicholas and Quine, 2010;Stokes et al, 2011). Both forms of equifinality have their origins in systems theory (von Bertalanffy, 1968) and has been identified and quantified in a range of geoscience settings (e.g. Beven and Binley, 1992;Kuczera and Parent, 1998;Romanowicz and Beven, 1998;Beven and Freer, 2001;Blazkova and Beven, 2004;Hunter et al, 2005;Hassan et al, 2008;Vasquez et al, 2009;Vrugt et al, 2009;Franz and Hogue, 2011).…”

Section: Equifinality In Numerical Modellingmentioning

confidence: 99%

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Numerical modelling of glacial lake outburst floods using physically based dam-breach models

et al. 2015

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Abstract. The instability of moraine-dammed proglacial lakes creates the potential for catastrophic glacial lake outburst floods (GLOFs) in high-mountain regions. In this research, we use a unique combination of numerical dam-breach and two-dimensional hydrodynamic modelling, employed within a generalised likelihood uncertainty estimation (GLUE) framework, to quantify predictive uncertainty in model outputs associated with a reconstruction of the Dig Tsho failure in Nepal. Monte Carlo analysis was used to sample the model parameter space, and morphological descriptors of the moraine breach were used to evaluate model performance. Multiple breach scenarios were produced by differing parameter ensembles associated with a range of breach initiation mechanisms, including overtopping waves and mechanical failure of the dam face. The material roughness coefficient was found to exert a dominant influence over model performance. The downstream routing of scenario-specific breach hydrographs revealed significant differences in the timing and extent of inundation. A GLUE-based methodology for constructing probabilistic maps of inundation extent, flow depth, and hazard is presented and provides a useful tool for communicating uncertainty in GLOF hazard assessment.

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Section: Hydrodynamic Solver Comparisonmentioning

confidence: 99%

Section: Equifinality In Numerical Modellingmentioning

confidence: 99%

Numerical modelling of glacial lake outburst floods using physically based dam-breach models

et al. 2015

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“…Finite-difference methods are the most frequently used numerical techniques to solve the unsteady flow equations (Abbott and Ionescu, 1967;Fread, 1973;Beam and Warming, 1976;Fennema and Chaudhry, 1986;Garcia and Kahawita, 15 1986;Venutelli, 2002). In such methods, the derivatives of the governing equations are approximated by a finite-difference formulation which is then substituted into the partial differential forms of the equations, thus transforming the governing equations into difference equations that are solved along a fixed rectangular x-t grid (Gates and AlZahrani, 1996a).…”

Section: Solution Methods For the Saint-venant Equationsmentioning

confidence: 99%

Ensemble modeling of stochastic unsteady open-channel flow in terms of its time-space evolutionary probability distribution: theoretical development

Dib¹,

Kavvas²

2017

Preprint

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“…The Saint-Venant equations, also known as the spatially varied unsteady flow equations (Sturm, 2001), are the two governing equations used to describe an unsteady open-channel flow problem that will be solved using the hydraulic routing technique (Chow, 1959;Viessman et al, 1977;Sturm, 2001). They consist of the continuity equation and the momentum equation which are used simultaneously in order to solve for the two unknowns (velocity and depth, or discharge and depth).…”

Section: Saint-venant Equations For Unsteady Open-channel Flowmentioning

confidence: 99%

Ensemble modeling of stochastic unsteady open-channel flow in terms of its time–space evolutionary probability distribution – Part 1: theoretical development

Dib¹,

Kavvas²

2018

Hydrol. Earth Syst. Sci.

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Abstract. The Saint-Venant equations are commonly used as the governing equations to solve for modeling the spatially varied unsteady flow in open channels. The presence of uncertainties in the channel or flow parameters renders these equations stochastic, thus requiring their solution in a stochastic framework in order to quantify the ensemble behavior and the variability of the process. While the Monte Carlo approach can be used for such a solution, its computational expense and its large number of simulations act to its disadvantage. This study proposes, explains, and derives a new methodology for solving the stochastic Saint-Venant equations in only one shot, without the need for a large number of simulations. The proposed methodology is derived by developing the nonlocal Lagrangian-Eulerian FokkerPlanck equation of the characteristic form of the stochastic Saint-Venant equations for an open-channel flow process, with an uncertain roughness coefficient. A numerical method for its solution is subsequently devised. The application and validation of this methodology are provided in a companion paper, in which the statistical results computed by the proposed methodology are compared against the results obtained by the Monte Carlo approach.

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Stability and Accuracy of Weighted Four-Point Implicit Finite Difference Schemes for Open Channel Flow

Cited by 42 publications

References 4 publications

Numerical modelling of glacial lake outburst floods using physically based dam-breach models

Numerical modelling of glacial lake outburst floods using physically based dam-breach models

Ensemble modeling of stochastic unsteady open-channel flow in terms of its time-space evolutionary probability distribution: theoretical development

Ensemble modeling of stochastic unsteady open-channel flow in terms of its time–space evolutionary probability distribution – Part 1: theoretical development

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