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A residual-based shock capturing scheme for the continuous/discontinuous spectral element solution of the 2D shallow water equations.

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Title: A residual-based shock capturing scheme for the continuous/discontinuous spectral element solution of the 2D shallow water equations.
Authors: Marras, Simone1 simone.marras@njit.edu, Kopera, Michal A.2, Constantinescu, Emil M.3,4, Suckale, Jenny1, Giraldo, Francis X.5
Source: Advances in Water Resources. Apr2018, Vol. 114, p45-63. 19p.
Subjects: Galerkin methods, Hydrologic models, Large eddy simulation models, Viscosity, Oscillations
Abstract: The high-order numerical solution of the non-linear shallow water equations is susceptible to Gibbs oscillations in the proximity of strong gradients. In this paper, we tackle this issue by presenting a shock capturing model based on the numerical residual of the solution. Via numerical tests, we demonstrate that the model removes the spurious oscillations in the proximity of strong wave fronts while preserving their strength. Furthermore, for coarse grids, it prevents energy from building up at small wave-numbers. When applied to the continuity equation to stabilize the water surface, the addition of the shock capturing scheme does not affect mass conservation. We found that our model improves the continuous and discontinuous Galerkin solutions alike in the proximity of sharp fronts propagating on wet surfaces. In the presence of wet/dry interfaces, however, the model needs to be enhanced with the addition of an inundation scheme which, however, we do not address in this paper. [ABSTRACT FROM AUTHOR]
Copyright of Advances in Water Resources is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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DbLabel: Engineering Source
An: 128474342
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  Data: A residual-based shock capturing scheme for the continuous/discontinuous spectral element solution of the 2D shallow water equations.
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  Data: <searchLink fieldCode="JN" term="%22Advances+in+Water+Resources%22">Advances in Water Resources</searchLink>. Apr2018, Vol. 114, p45-63. 19p.
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  Data: <searchLink fieldCode="DE" term="%22Galerkin+methods%22">Galerkin methods</searchLink><br /><searchLink fieldCode="DE" term="%22Hydrologic+models%22">Hydrologic models</searchLink><br /><searchLink fieldCode="DE" term="%22Large+eddy+simulation+models%22">Large eddy simulation models</searchLink><br /><searchLink fieldCode="DE" term="%22Viscosity%22">Viscosity</searchLink><br /><searchLink fieldCode="DE" term="%22Oscillations%22">Oscillations</searchLink>
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  Data: The high-order numerical solution of the non-linear shallow water equations is susceptible to Gibbs oscillations in the proximity of strong gradients. In this paper, we tackle this issue by presenting a shock capturing model based on the numerical residual of the solution. Via numerical tests, we demonstrate that the model removes the spurious oscillations in the proximity of strong wave fronts while preserving their strength. Furthermore, for coarse grids, it prevents energy from building up at small wave-numbers. When applied to the continuity equation to stabilize the water surface, the addition of the shock capturing scheme does not affect mass conservation. We found that our model improves the continuous and discontinuous Galerkin solutions alike in the proximity of sharp fronts propagating on wet surfaces. In the presence of wet/dry interfaces, however, the model needs to be enhanced with the addition of an inundation scheme which, however, we do not address in this paper. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
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  Data: <i>Copyright of Advances in Water Resources is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Type: doi
        Value: 10.1016/j.advwatres.2018.02.003
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 19
        StartPage: 45
    Subjects:
      – SubjectFull: Galerkin methods
        Type: general
      – SubjectFull: Hydrologic models
        Type: general
      – SubjectFull: Large eddy simulation models
        Type: general
      – SubjectFull: Viscosity
        Type: general
      – SubjectFull: Oscillations
        Type: general
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      – TitleFull: A residual-based shock capturing scheme for the continuous/discontinuous spectral element solution of the 2D shallow water equations.
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            NameFull: Suckale, Jenny
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            NameFull: Giraldo, Francis X.
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              Text: Apr2018
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              Y: 2018
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