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A spectral/hp element depth-integrated model for nonlinear wave-body interaction

Abstract : We present a spectral/hp element method for a depth-integrated Boussinsq model for the efficient simulation of nonlinear wave-body interaction. The model exploits a `unified' Boussinesq framework, i.e. the flow under the body is also treated with the depth-integrated approach, initially proposed by (Jiang, 2001) and more recently rigorously analysed by (Lannes, 2016). The choice of the Boussinesq equations allows the elimination of the vertical dimension, resulting in a wave-body model with an adequate precision for weakly nonlinear and dispersive waves expressed in horizontal dimensions only. The framework involves the coupling of two different domains with different flow characteristics. In this work we employ flux-based conditions for domain coupling, following the recipes provided by the discontinuous Galerkin spectral/hp element framework. Inside each domain, the continuous spectral/hp element method is used to solve the appropriate flow model. The spectral/hp element method allows to achieve high-order, possibly exponential, convergence for non-breaking waves and account for the nonlinear interaction with fixed and floating bodies. Our main contribution is to include floating surface-piercing bodies in the conventional depth-integrated Boussinesq framework and the use of a spectral/hp element method for high-order accurate numerical discretization in space. The model is validated against published results for wave-body interaction and confirmed to have excellent accuracy. The proposed nonlinear model is demonstrated to be relevant for the simulation of wave energy devices.
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https://hal.inria.fr/hal-01760366
Contributor : Mario Ricchiuto <>
Submitted on : Friday, April 6, 2018 - 4:29:54 PM
Last modification on : Friday, November 16, 2018 - 3:02:06 PM

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Umberto Bosi, Allan Peter Engsig-Karup, Claes Eskilsson, Mario Ricchiuto. A spectral/hp element depth-integrated model for nonlinear wave-body interaction. [Research Report] RR-9166, Inria Bordeaux Sud-Ouest; Technical University of Denmark; University of Aalborg; RISE. 2018. ⟨hal-01760366⟩

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