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A spectral/hp element depth-integrated model for nonlinear wave–body interaction
INRIA Bordeaux Sud-Ouest, France.
DTU Technical University of Denmark, Denmark.
RISE - Research Institutes of Sweden, Safety and Transport, Safety. Aalborg University, Denmark.ORCID iD: 0000-0001-6934-634x
INRIA Bordeaux Sud-Ouest, France.
2019 (English)In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 348, p. 222-249Article in journal (Refereed) Published
Abstract [en]

We present a depth-integrated Boussinesq model for the efficient simulation of nonlinear wave–body interaction. The model exploits a ‘unified’ Boussinesq framework, i.e. the fluid under the body is also treated with the depth-integrated approach. The unified Boussinesq approach was initially proposed by Jiang (2001) and recently analyzed by Lannes (2017). The choice of Boussinesq-type equations removes the vertical dimension of the problem, resulting in a wave–body model with 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. Inside each domain, the continuous spectral/hp element method is used to solve the appropriate flow model since it allows to achieve high-order, possibly exponential, convergence for non-breaking waves. Flux-based conditions for the domain coupling are used, following the recipes provided by the discontinuous Galerkin framework. The main contribution of this work is the inclusion of 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 verified using manufactured solutions and validated against published results for wave–body interaction. The model is shown to have excellent accuracy and is relevant for applications of waves interacting with wave energy devices.

Place, publisher, year, edition, pages
2019. Vol. 348, p. 222-249
Keywords [en]
Boussinesq equations, Discontinuous Galerkin method, Domain decomposition, Nonlinear and dispersive waves, Spectral/hp element method, Wave–body interaction, Coastal engineering, Dispersion (waves), Domain decomposition methods, Galerkin methods, Nonlinear equations, Numerical methods, Wave energy conversion, Boussinesq-type equations, Depth-integrated models, Discontinuous galerkin, Discontinuous Galerkin methods, Dispersive waves, Numerical discretization, Water waves
National Category
Natural Sciences
Identifiers
URN: urn:nbn:se:ri:diva-37856DOI: 10.1016/j.cma.2019.01.020Scopus ID: 2-s2.0-85061346648OAI: oai:DiVA.org:ri-37856DiVA, id: diva2:1292990
Note

 Funding details: Conseil Régional Aquitaine; Funding details: Institute for Mind and Body, University of Chicago, IMB; Funding details: Fuel Cell Technologies Program, FCT; Funding details: Centre National de la Recherche Scientifique, CNRS; Funding text 1: This work was performed within the Ocean ERANET project MIDWEST, funded by the French agency ADEME , Swedish Agency SWEA and Portuguese agency FCT . We warmly thank Dr. D. Lannes for many useful and interesting discussions and suggestions. Some of the numerical simulations presented in this paper were carried out using the PlaFRIM platform, supported by Inria, CNRS (LABRI and IMB), Université de Bordeaux, Bordeaux INP and Conseil Régional d’Aquitaine (see https://www.plafrim.fr/ ).

Available from: 2019-03-01 Created: 2019-03-01 Last updated: 2019-06-27Bibliographically approved

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