Development of a hyperbolic dispersive model for coastal waves - Implementation in TOLOSA

  • Duran, Arnaud (ICJ, Université Claude Bernard Lyon 1.)
  • Baraille, Rémy (IMT, Université de Toulouse, CNRS, INSA.)
  • Couderc, Frédéric (IMT, Université de Toulouse, CNRS, INSA.)
  • Hung, Yen-Chung (LAMA, Universit Savoie Mont-Blanc, Chambéry.)
  • Kazakova, Maria (LAMA, Universit Savoie Mont-Blanc, Chambéry.)
  • Richard, Gaël (Université Grenoble Alpes, INRAE, UR ETNA, Grenoble.)
  • Vila, Jean-Paul (IMT, Université de Toulouse, CNRS, INSA.)

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Depth-averaged models are one of the classic approaches for coastal wave modeling. Dispersive models of this type are called Boussinesq type models to which the fully nonlinear model of Serre-Green-Naghdi (SGN) belongs. All these models are of mixed elliptic-hyperbolic type and require an elliptical step in their numerical resolution. This step leads to a significant increase in computation time as well as difficulties of implementation and management of boundary conditions. In recent work, a compressible dispersive model has been derived, which can be seen as a hyperbolic approximation of the SGN equations. Improved dispersive properties can be obtained without breaking the structure of the system, and the same applies to a new strategy recently developed to describe breaking waves for SGN. The hyperbolic nature of the model provides a framework particularly suitable for numerical resolution, allowing to overcome the technical limitations mentioned above. In addition, recent techniques can be easily adapted to ensure non-linear stability (discrete decrease of mechanical energy), while minimizing diffusive losses. These properties are fundamental for the targeted operational contexts. On this basis, it is possible to propose several variants of stable and low-diffusive 2d numerical schemes on unstructured meshes, exhibiting an excellent compromise between accuracy and algorithmic complexity. Given the level of performance and ease of implementation provided by the approach, it is currently being studied with a view to its use for operational purposes. In the long term, this model is intended to be implemented in the TOLOSA code developed for forecasting and preventing the risk of marine submersion in conjunction with SHOM (Service Hydrographique et Ocanographique de la Marine) and Meteo France.