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Implementation and Evaluation of Breaking Detection Criteria for a Hybrid Boussinesq Model

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Abstract

The aim of the present work has been to develop a model able to represent the propagation and transformation of waves in nearshore areas. The focus is on the phenomena of wave breaking, shoaling, and run-up. These different phenomena are represented through a hybrid approach obtained by the coupling of non-linear Shallow Water equations with the extended Boussinesq equations of Madsen and Sørensen. The novelty is the switch tool between the two modelling equations: a critical free surface Froude criterion. This is based on a physically meaningful new approach to detect wave breaking, which corresponds to the steepening of the wave’s crest which turns into a roller. To allow for an appropriate discretization of both types of equations, we consider a finite element Upwind Petrov Galerkin method with a novel limiting strategy that guarantees the preservation of smooth waves as well as the monotonicity of the results in presence of discontinuities. We provide a detailed discussion of the implementation of the newly proposed detection method, as well as of two other well-known criteria which are used for comparison. An extensive benchmarking on several problems involving different wave phenomena and breaking conditions allows to show the robustness of the numerical method proposed, as well as to assess the advantages and limitations of the different detection methods.

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Notes

  1. Matrix absolute values are computed, as usual, by means of an eigen-decomposition.

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Authors and Affiliations

  1. Institute of Mathematics, University of Zurich, Winterthurerstrasse 190, 8057, Zürich, Switzerland

    Paola Bacigaluppi

  2. Team CARDAMOM, Inria Bordeaux Sud-Ouest, 200 avenue de la Vieille Tour, 33405, Talence Cedex, France

    Mario Ricchiuto

  3. University of Bordeaux, CNRS, UMR 5805 EPOC, Allée Geoffroy Saint-Hilaire, 33615, Pessac, France

    Philippe Bonneton

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  1. Paola Bacigaluppi
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Correspondence to Paola Bacigaluppi.

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Bacigaluppi, P., Ricchiuto, M. & Bonneton, P. Implementation and Evaluation of Breaking Detection Criteria for a Hybrid Boussinesq Model. Water Waves 2, 207–241 (2020). https://doi.org/10.1007/s42286-019-00023-8

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