This work investigates the topical problem of balancing the shallow water equations over bottom steps of different heights. The current approaches in the literature are essentially based on mathematical analysis of the hyperbolic system of balance equations and take into account the relevant progresses in treating the non-conservative form of the governing system in the framework of path-conservative schemes. An important problem under debate is the correct position of the momentum balance closure when the bottom elevation is discontinuous. Cases of technical interest are systematically analysed, consisting of backward-facing steps and forward-facing steps, tackled supercritical and subcritical flows; critical (sonic) conditions are also analysed and discussed. The fundamental concept governing the problem and supported by the present computations is that the energy-conserving approach is the only approach that is consistent with the classical shallow water equations formulated with geometrical source terms and that the momentum balance is properly closed if a proper choice of a conventional depth on the bottom step is performed. The depth on the step is shown to be included between the depths just upstream and just downstream of the step. It is also shown that current choices (as given in the literature) of the depth on (or in front of) the step can lead to unphysical configurations, similar to some energy-increasing solutions.

Momentum balance in the shallow water equations on bottom discontinuities

VALIANI, Alessandro
Primo
;
CALEFFI, Valerio
Ultimo
2017

Abstract

This work investigates the topical problem of balancing the shallow water equations over bottom steps of different heights. The current approaches in the literature are essentially based on mathematical analysis of the hyperbolic system of balance equations and take into account the relevant progresses in treating the non-conservative form of the governing system in the framework of path-conservative schemes. An important problem under debate is the correct position of the momentum balance closure when the bottom elevation is discontinuous. Cases of technical interest are systematically analysed, consisting of backward-facing steps and forward-facing steps, tackled supercritical and subcritical flows; critical (sonic) conditions are also analysed and discussed. The fundamental concept governing the problem and supported by the present computations is that the energy-conserving approach is the only approach that is consistent with the classical shallow water equations formulated with geometrical source terms and that the momentum balance is properly closed if a proper choice of a conventional depth on the bottom step is performed. The depth on the step is shown to be included between the depths just upstream and just downstream of the step. It is also shown that current choices (as given in the literature) of the depth on (or in front of) the step can lead to unphysical configurations, similar to some energy-increasing solutions.
2017
Valiani, Alessandro; Caleffi, Valerio
File in questo prodotto:
File Dimensione Formato  
Momentum balance in the shallow water equations on bottom discontinuities.pdf

solo gestori archivio

Descrizione: Momentum balance in the shallow water equations on bottom discontinuities
Tipologia: Full text (versione editoriale)
Licenza: NON PUBBLICO - Accesso privato/ristretto
Dimensione 1.86 MB
Formato Adobe PDF
1.86 MB Adobe PDF   Visualizza/Apri   Richiedi una copia
momentum balance in the shallow water equations on bottom discontinuities.pdf

accesso aperto

Tipologia: Pre-print
Licenza: Creative commons
Dimensione 716.42 kB
Formato Adobe PDF
716.42 kB Adobe PDF Visualizza/Apri

I documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11392/2368150
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 14
  • ???jsp.display-item.citation.isi??? 13
social impact