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  • Volume 14, Issue 3

A well-balanced spectral volume scheme with the wetting–drying property for the shallow-water equations

Luca Cozzolino, Renata Della Morte, Giuseppe Del Giudice, Anna Palumbo, Domenico Pianese
Published July 2012, 14 (3) 745-760; DOI: 10.2166/hydro.2012.035
Luca Cozzolino
Dipartimento per le Tecnologie, Università degli Studi di Napoli Parthenope, Centro Direzionale di Napoli, Isola C4, I-80143 Napoli, Italy E-mail: luca.cozzolino@uniparthenope.it
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Renata Della Morte
Dipartimento per le Tecnologie, Università degli Studi di Napoli Parthenope, Centro Direzionale di Napoli, Isola C4, I-80143 Napoli, Italy E-mail: luca.cozzolino@uniparthenope.it
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Giuseppe Del Giudice
Dipartimento di Ingegneria Idraulica Geotecnica e Ambientale, Università degli Studi di Napoli Federico II, via Claudio 21, I-80125 Napoli, Italy
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Anna Palumbo
Dipartimento di Ingegneria Idraulica Geotecnica e Ambientale, Università degli Studi di Napoli Federico II, via Claudio 21, I-80125 Napoli, Italy
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Domenico Pianese
Dipartimento di Ingegneria Idraulica Geotecnica e Ambientale, Università degli Studi di Napoli Federico II, via Claudio 21, I-80125 Napoli, Italy
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Abstract

The shallow-water equations are widely used to model surface water bodies, such as lakes, rivers and the swash zone in coastal flows. Physically congruent solutions are characterized by non-negative water depth, and many numerical methods may fail to preserve this property at the discrete level when moving wet–dry transitions are present in the physical domain. In this paper, we present a spectral-volume method for the approximate solution of the one-dimensional shallow-water equations, which is third-order accurate in wet regions, far from discontinuities, and which is well balanced for water at rest states: the stability of the solution is ensured if reconstruction and limitation of variables preserves non-negativity of the depth and a suitable constraint for the time step length is satisfied. A number of numerical experiments are reported, showing the promising capabilities of the model to solve problems with non-trivial topographies and friction.

  • friction
  • high-order accuracy
  • shallow-water equations
  • spectral volume method
  • well-balancing property
  • wetting–drying property
  • First received 25 March 2011.
  • Accepted in revised form 5 October 2011.
  • © IWA Publishing 2012
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Journal of Hydroinformatics: 20 (2)
  Volume 14, Issue 3

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A well-balanced spectral volume scheme with the wetting–drying property for the shallow-water equations
Luca Cozzolino, Renata Della Morte, Giuseppe Del Giudice, Anna Palumbo, Domenico Pianese
Journal of Hydroinformatics Jul 2012, 14 (3) 745-760; DOI: 10.2166/hydro.2012.035
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A well-balanced spectral volume scheme with the wetting–drying property for the shallow-water equations
Luca Cozzolino, Renata Della Morte, Giuseppe Del Giudice, Anna Palumbo, Domenico Pianese
Journal of Hydroinformatics Jul 2012, 14 (3) 745-760; DOI: 10.2166/hydro.2012.035

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Keywords

friction
high-order accuracy
shallow-water equations
spectral volume method
well-balancing property
wetting–drying property
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