Use of Clement’s ODEs for the speedup of computation of the Green function and its derivatives for floating of submerged bodies in deep water

• Published in: Volume 7A: Ocean Engineering
• Main Authors: Xie, Chunmei, Babarit, Aurélien, Rongère, François, Clément, Alain H.
• Other Authors: Laboratoire de recherche en Hydrodynamique, Énergétique et Environnement Atmosphérique (LHEEA), École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS)
• Format: Conference Object
• Language: English
• Published: HAL CCSD 2018
• Subjects: [SPI.MECA.MEFL]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph]; [SPI.NRJ]Engineering Sciences [physics]/Electric power; Arctic
• Online Access: https://hal.science/hal-01986164; https://hal.science/hal-01986164/document; https://hal.science/hal-01986164/file/xie2018.pdf; https://doi.org/10.1115/OMAE2018-78295

ASME 2018 37th International Conference on Ocean, Offshore and Arctic EngineeringVolume 7A: Ocean EngineeringConference Sponsors: Ocean, Offshore and Arctic Engineering DivisionISBN: 978-0-7918-5126-5 International audience A new acceleration technique for the computation of first order hydrodynamic coefficients for floating bodies in frequency domain and in deep water is proposed. It is based on the classical boundary element method (BEM) which requires solving a boundary integral equation for distributions of sources and/or dipoles and evaluating integrals of Kelvin’s Green function and its derivatives over panels. The Kelvin’s Green function includes two Rankine sources and a wave term. In present study, for the two Rankine sources, analytical integrations of strongly singular kernels are adopted for the linear density distributions. It is shown that these analytical integrations are more accurate and faster than numerical integrations. The wave term is obtained by solving Clément’s ordinary differential equations (ODEs) [1] and an adaptive numerical quadrature is performed for integrations over the panels. It is shown here that the computational time of the wave term by solving the ODEs is greatly reduced compared to the classical integration method [7].