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Non-linear shallow water flow modelling over topography with depth-averaged potential equations

Environmental fluid mechanics (Dordrecht, Netherlands : 2001), 2020-04, Vol.20 (2), p.261-291

Springer Nature B.V. 2019 ;Springer Nature B.V. 2019. ;ISSN: 1567-7419 ;EISSN: 1573-1510 ;DOI: 10.1007/s10652-019-09691-z

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Title:
Non-linear shallow water flow modelling over topography with depth-averaged potential equations
Author: Castro-Orgaz, Oscar ; Cantero-Chinchilla, Francisco N.
Subjects: Boussinesq approximation ; Boussinesq equations ; Channel flow ; Classical Mechanics ; Computational fluid dynamics ; Continuum mechanics ; Depth ; Earth and Environmental Science ; Earth Sciences ; Environmental Physics ; Equations ; Flow theory ; Fluid flow ; Fluid mechanics ; Hydrogeology ; Hydrology/Water Resources ; Ideal fluids ; Iterative methods ; Mathematical models ; Modelling ; Momentum ; Numerical schemes ; Oceanography ; Open channel flow ; Open channels ; Original Article ; Picard iterations ; Shallow water ; Steady flow ; Topography ; Topography (geology) ; Transcritical flow ; Two dimensional models ; Water depth ; Water flow ; Weirs
Is Part Of: Environmental fluid mechanics (Dordrecht, Netherlands : 2001), 2020-04, Vol.20 (2), p.261-291
Description: Hunter Rouse was the father of the Fluid Mechanics of Open Channel Flow . In this review article the fundamental advances on the non-hydrostatic modeling of shallow open channel flow over topography, since the publication of his 1938 book, are discussed. Flows over uneven topography, like at open channel controls, occurs in a short length, thus rendering ideal fluid flow theory an adequate mathematical tool. This paper emphasis is on depth-averaged modeling of these flows using Boussinesq equations, given the significant advances basically since the 80’s. The one-dimensional steady flow model from Picard iteration is reviewed in detail, including energy and momentum formulations, flow at a weir crest, and on a slope. A new numerical scheme is developed for the solution of transcritical steady weir flow, showing excellent match with experiments. A new derivation for the two-dimensional depth-averaged unsteady ideal fluid model is presented based on a continuum mechanics formulation. The result is the Serre–Green–Naghdi equations (SGNE). It is demonstrated that the extended Bernoulli equation derived from Picard iteration is an integral form of the SGNE for 1D steady flow. A robust MUSCL-Hancock finite volume model is developed to solve the unsteady 1D SGNE, showing excellent agreement with the steady transcritical flow solutions previously constructed. The accuracy of the MUSCL-Hancock solver is critically assessed using a higher-order solver for the SGNE.
Publisher: Dordrecht: Springer Netherlands
Language: English
Identifier: ISSN: 1567-7419
EISSN: 1573-1510
DOI: 10.1007/s10652-019-09691-z
Source: AUTh Library subscriptions: ProQuest Central

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Non-linear shallow water flow modelling over topography with depth-averaged potential equations

Springer Nature B.V. 2019 ;Springer Nature B.V. 2019. ;ISSN: 1567-7419 ;EISSN: 1573-1510 ;DOI: 10.1007/s10652-019-09691-z

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