Efficient Algorithm for Gradually Varied Flows in Channel Networks

Sen, Debabrata; Garg, Navneet

doi:10.1061/(asce)0733-9437(2002)128:6(351)

Cited by 47 publications

(39 citation statements)

References 13 publications

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“…The literature with these two methods is vast, but a reasonable cross section is provided in Table 1. Beyond these two major families, a variety of other schemes have been applied including finiteelement methods (e.g., Szymkiewicz, 1991;Venutelli, 2003), finite-volume methods that do not use the Godunov approach (e.g., Audusse et al, 2004Audusse et al, , 2016Catella et al, 2008;Katsaounis et al, 2004;Mohamed, 2014;Vazquez-Cendon, 1999;Xing and Shu, 2011;Ying et al, 2004), and finitedifference methods that do not apply the Preissmann scheme (e.g., Abbott and Ionescu, 1967;Aricò and Tucciarelli, 2007;Buntina and Ostapenko, 2008;Schippa and Pavan, 2008;Tucciarelli, 2003;Wang et al, 2000). A recent development is the introduction of discontinuous Galerkin (DG) methods, which can be thought of as a higher-order Godunov method (e.g., Kesserwani et al, 2008Kesserwani et al, , 2009Lai and Khan, 2012;Xing, 2014;Xing and Zhang, 2013).…”

Section: Preissmann Vs Godunovmentioning

confidence: 99%

Conservative finite-volume forms of the Saint-Venant equations for hydrology and urban drainage

Hodges

2019

Hydrol. Earth Syst. Sci.

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Abstract. New integral, finite-volume forms of the Saint-Venant equations for one-dimensional (1-D) open-channel flow are derived. The new equations are in the flux-gradient conservation form and transfer portions of both the hydrostatic pressure force and the gravitational force from the source term to the conservative flux term. This approach prevents irregular channel topography from creating an inherently non-smooth source term for momentum. The derivation introduces an analytical approximation of the free surface across a finite-volume element (e.g., linear, parabolic) with a weighting function for quadrature with bottom topography. This new free-surface/topography approach provides a single term that approximates the integrated piezometric pressure over a control volume that can be split between the source and the conservative flux terms without introducing new variables within the discretization. The resulting conservative finite-volume equations are written entirely in terms of flow rates, cross-sectional areas, and water surface elevations – without using the bottom slope (S0). The new Saint-Venant equation form is (1) inherently conservative, as compared to non-conservative finite-difference forms, and (2) inherently well-balanced for irregular topography, as compared to conservative finite-volume forms using the Cunge–Liggett approach that rely on two integrations of topography. It is likely that this new equation form will be more tractable for large-scale simulations of river networks and urban drainage systems with highly variable topography as it ensures the inhomogeneous source term of the momentum conservation equation is Lipschitz smooth as long as the solution variables are smooth.

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Section: Preissmann Vs Godunovmentioning

confidence: 99%

Conservative finite-volume forms of the Saint-Venant equations for hydrology and urban drainage

Hodges

2019

Hydrol. Earth Syst. Sci.

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“…Si se trata de canales paralelos o redes de canales, entonces el sistema deberá incluir las ecuaciones de continuidad en los sitios donde un canal se separa en dos o más, y donde se unen dos o más canales. Existe un limitado número de algoritmos para resolver sistemas de canales [2,3,4], sin embargo los mismos han sido de poco alcance ya que solamente resuelven por caudales y profundidades del agua en los canales, sin considerar estructuras para distribución o control del agua. Es común que en un sistema de canales existan estructuras hidráulicas tales como vertedores, compuertas y sifones invertidos.…”

Section: Metodologíaunclassified

“…Este método aproxima la solución iterativamente resolviendo las ecuaciones linealizadas sucesivamente hasta tener convergencia [6]. 4. Las ecuaciones lineales se resuelven con el método Gradiente Biconjugado Estabilizado con Precondicionador (BiCGSTAB por sus siglas en inglés) el cual es apropiado para sistemas lineales, no-simétricos y con matrices dispersas [7].…”

Section: Metodologíaunclassified

Modelo Hidráulico para Redes de Canales con Estructuras Hidráulicas

Santiago-Collazo¹,

Araya²

2019

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Redes de canales; flujo gradualmente variado; método de solución simultánea para canales; análisis y diseño de estructuras hidráulicas. ResumenMuchos sistemas de irrigación contienen sistemas de canales complejos que incluyen estructuras de control. La regulación y control de la distribución de agua para regar los cultivos es necesaria para una agricultura sostenible. El diseño y análisis de estructuras hidráulicas es esencial para la conservación y el uso eficiente del agua dentro del sistema. Este artículo presenta las capacidades de un modelo hidráulico para resolver redes de canales con estructuras hidráulicas. El algoritmo utiliza el Método de Solución Simultanea (MSS) para resolver las ecuaciones de continuidad y energía en varios tramos del canal. Los resultados obtenidos incluyen profundidades del agua, distribución de flujos y dimensionamiento de estructuras hidráulicas. Se presentan dos aplicaciones: la modelación de un tramo del Distrito de Riego del Valle de Lajas (DRVL) de Puerto Rico y una red de canales con diseño y análisis de diferentes estructuras hidráulicas. El MSS ha probado ser excelente para aplicaciones prácticas debido a su fácil uso, capacidades y precisión. KeywordsChannel network; gradually-varied flow; simultaneous solution method; analysis and design of hydraulic structures. AbstractMany irrigation systems comprise complex channel systems including control structures. Regulation and control of water distribution for crop irrigation is necessary for sustainable agriculture. Design and analysis of hydraulic structures is essential for efficient use and conservation of water. This article presents the capabilities of a hydraulic model for solution of channel networks with hydraulic structures. The algorithm uses the Simultaneous Solution Method (SSM) to solve the continuity and energy equations in several channel reaches. The results include water depths, distribution of flows and dimensions of hydraulic structures. Two applications are presented: modeling of a reach of the Lajas Valley Irrigation System in Puerto Rico and, a channel network with design and analysis of different hydraulic structures. The SSM proved to be excellent for practical applications due to ease of use, capabilities and precision.

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“…The SV equations may account for flows of variable widths and depths, for example, in floodplains Beltaos et al, 2012), rivers (Guinot and Cappelaere, 2009), overland flow (Berger and Stockstill, 1995;Ghavasieh et al, 2006;Kirstetter et al, 2016), overpressure in drainage systems (Henine et al, 2014), man-made channels (Zhou, 1995;Sen and Garg, 2002;Sau et al, 2010), vegetation flushing , channel networks (Choi and Molinas, 1993;Camacho and Lees, 1999;Saleh et al, 2013), on benchmarks , interaction with subsurfaces (Pan et al, 2015), or natural settings (Moussa and Bocquillon, 1996a;Wang and Chen, 2003;Roux and Dartus, 2006;Burguete et al, 2008;, including these with curved boundaries (Sivakumaran and Yevjevich, 1987). Discharge and cross-sectional area may conveniently be used instead of velocity and water depth, and the two equations describing mass and momentum in the Saint-Venant system are now written as )…”

Section: Water Flowmentioning

confidence: 99%

Determinants of modelling choices for 1-D free-surface flow and morphodynamics in hydrology and hydraulics: a review

Cheviron

Moussa²

2016

Hydrol. Earth Syst. Sci.

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Abstract. This review paper investigates the determinants of modelling choices, for numerous applications of 1-D freesurface flow and morphodynamic equations in hydrology and hydraulics, across multiple spatiotemporal scales. We aim to characterize each case study by its signature composed of model refinement (Navier-Stokes: NS; Reynolds-averaged Navier-Stokes: RANS; Saint-Venant: SV; or approximations to Saint-Venant: ASV), spatiotemporal scales and subscales (domain length: L from 1 cm to 1000 km; temporal scale: T from 1 s to 1 year; flow depth: H from 1 mm to 10 m; spatial step for modelling: δL; temporal step: δT ), flow typology (Overland: O; High gradient: Hg; Bedforms: B; Fluvial: F), and dimensionless numbers (dimensionless time period T * , Reynolds number Re, Froude number Fr, slope S, inundation ratio z , Shields number θ ). The determinants of modelling choices are therefore sought in the interplay between flow characteristics and cross-scale and scale-independent views. The influence of spatiotemporal scales on modelling choices is first quantified through the expected correlation between increasing scales and decreasing model refinements (though modelling objectives also show through the chosen spatial and temporal subscales). Then flow typology appears a secondary but important determinant in the choice of model refinement. This finding is confirmed by the discriminating values of several dimensionless numbers, which prove preferential associations between model refinements and flow typologies. This review is intended to help modellers in positioning their choices with respect to the most frequent practices, within a generic, normative procedure possibly enriched by the community for a larger, comprehensive and updated image of modelling strategies.

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Efficient Algorithm for Gradually Varied Flows in Channel Networks

Cited by 47 publications

References 13 publications

Conservative finite-volume forms of the Saint-Venant equations for hydrology and urban drainage

Conservative finite-volume forms of the Saint-Venant equations for hydrology and urban drainage

Modelo Hidráulico para Redes de Canales con Estructuras Hidráulicas

Determinants of modelling choices for 1-D free-surface flow and morphodynamics in hydrology and hydraulics: a review

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