Conditions governing the use of approximations for the Saint-Vénant equations for shallow surface water flow

Vieira, Jardel

doi:10.1016/0022-1694(83)90013-6

Cited by 150 publications

(84 citation statements)

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“…System (1)- (2) is written in conservative form in the unknowns h, uh, and vh. Neglecting the inertial terms in the momentum Equations (2) and (3), which is equivalent to set g = ∞ (i.e., subcritical flow [9]), the 0ISWEs are given by Equation (1) and the new momentum Equation (4),…”

Section: The Governing Equationsmentioning

confidence: 99%

“…The last identity in Equation (4) is derived from simple manipulations of the two momentum equations. Merging Equation (4) in Equation (1) …”

Section: The Governing Equationsmentioning

confidence: 99%

“…According to the forms of the momentum equations of the SWEs, we classify the mathematical form of the governing equations as fully dynamic (FDSWEs), quasi-steady dynamic (QSWEs), zero-convective inertia (0CISWEs), zero-inertia (0ISWEs), and kinematic (KSWEs), respectively [4][5][6]. All the terms are retained in the momentum equation of the FDSWEs, the local inertial terms (or local accelerations) are neglected in the QSWEs, the convective inertial terms (or convective accelerations) are neglected in the 0CISWEs and, if both the local and convective accelerations are neglected, the system reduces to the 0ISWEs.…”

Section: Introductionmentioning

confidence: 99%

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Comparative Analyses between the Zero-Inertia and Fully Dynamic Models of the Shallow Water Equations for Unsteady Overland Flow Propagation

Aricò

Nasello

2018

Water

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Abstract:The shallow water equations are a mathematical tool widely applied for the simulation of flow routing in rivers and floodplains, as well as for flood inundation mapping. The interest of many researchers has been focused on the study of simplified forms of the original set of equations. One of the most commonly applied simplifications consists of neglecting the inertial terms. The effects of such a choice on the outputs of the simulations of flooding events are controversial and are an important topic of debate. In the present paper, two numerical models recently proposed for the solution of the complete and zero-inertia forms of the shallow water equations, are applied to several unsteady flow routing scenarios. We simulate synthetic and laboratory scenarios of unsteady flow routing, starting from very simple geometries and gradually moving towards complex topographies. Unlike the studies of the range of validity of the zero-inertia model, based on a small perturbation of the linearized flow model, in unsteady flow propagation over irregular topographies, it is more difficult to specify criteria for the applicability of the simplified set of equations. In analyzing the role of the terms in the momentum equations, we try to understand the effect of neglecting the inertial terms in the zero-inertia formulation. We also analyze the computational costs.

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Section: The Governing Equationsmentioning

confidence: 99%

“…The last identity in Equation (4) is derived from simple manipulations of the two momentum equations. Merging Equation (4) in Equation (1) …”

Section: The Governing Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Comparative Analyses between the Zero-Inertia and Fully Dynamic Models of the Shallow Water Equations for Unsteady Overland Flow Propagation

Aricò

Nasello

2018

Water

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“…The equations that describe the propagation of a flood wave with respect to distance along the channel and time in open channels are the so-called Saint-Venant equations, consisting of the continuity equation and the momentum equation. For most flood events, in most rivers the inertial terms appearing in the momentum equation of the Saint-Venant equations can be neglected as they are relatively smaller than the terms arising from gravity and resistance forces (Henderson, 1963;Dooge and Harley, 1967;Daluz Viera, 1983), leading to a simplified model of open channel flow. The diffusion wave equation is then expressed as (e.g.…”

Section: Description Of the Problemmentioning

confidence: 99%

Variability of flow discharge in lateral inflow-dominated stream channels

Chang

Yeh

2015

Hydrol. Earth Syst. Sci.

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Abstract. The influence of the temporal changes in lateral inflow rate on the discharge variability in stream channels is explored through the analysis of the diffusion wave equation (i.e. the linearized Saint-Venant equation). To account for variability and uncertainty, the lateral inflow rate is regarded as a temporal random function. On the basis of the spectral representation theory, analytical expressions for the covariance function and evolutionary power spectral density of the random discharge perturbation process are derived to quantify variability in stream flow discharge induced by the temporal changes in lateral inflow rate. The treatment of the discharge variance (square root of the variance) gives us a quantitative estimate of uncertainty in predictions from the deterministic model. It is found that the discharge variability of stream flow is very large in the downstream reach, indicating large uncertainty anticipated from the use of the deterministic model. A larger temporal correlation scale of inflow rate fluctuations, representing more temporal consistency of fluctuations in inflow rate around the mean, introduces a higher variability in stream flow discharge.

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“…The simplified equations should be chosen whenever the physical conditions justified them. Among these, the two common models are the diffusion wave and the kinematic wave approximations [1,2] .…”

Section: Introductionmentioning

confidence: 99%

The numerical simulation of one-dimensional overland flow by Lattice Boltzmann Method

Liu¹

2015

Proceedings of the 5th International Conference on Advanced Design and Manufacturing Engineering

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Conditions governing the use of approximations for the Saint-Vénant equations for shallow surface water flow

Cited by 150 publications

References 4 publications

Comparative Analyses between the Zero-Inertia and Fully Dynamic Models of the Shallow Water Equations for Unsteady Overland Flow Propagation

Comparative Analyses between the Zero-Inertia and Fully Dynamic Models of the Shallow Water Equations for Unsteady Overland Flow Propagation

Variability of flow discharge in lateral inflow-dominated stream channels

The numerical simulation of one-dimensional overland flow by Lattice Boltzmann Method

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