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Proof of the equivalence of Tanizawa–Berkvens’ and Cointe–van Daalen's formulations for the time derivative of the velocity potential for non-linear potential flow solvers |
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| Institution: | 1. Department of Marine Technology, NTNU, 7491 Trondheim, Norway;2. Multiconsult, Nedre Skøyen vei 2, 0213 Oslo, Norway;3. Department of Structural Engineering, NTNU, 7491 Trondheim, Norway;1. Naval Architecture and Marine Engineering Unit, DITEN, University of Genoa, Italy;2. Department of Aerospace and Ocean Engineering, Virginia Tech, Blacksburg, VA, USA;1. Department of Mathematics, Faculty of Mathematical and Physical Sciences, University College London, Gower Street, London, WC1E 6BT, UK;2. University College Dublin, School of Mathematical Sciences, Belfield, Dublin 4, Ireland;3. LAMA, UMR 5127 CNRS, Université de Savoie, Campus Scientifique, 73376 Le Bourget-du-Lac Cedex, France |
| Abstract: | Dealing with freely-floating bodies in the framework of non-linear potential flow theory may require solving Laplace's equation for the time derivative of the velocity potential. At present, there are two competing formulations for the body boundary condition. The first one was derived by Cointe 1] in 2D. It was later extended to 3D by van Daalen 2]. The second formulation was derived by Tanizawa 3] in 2D. It was extended to 3D by Berkvens 4]. In this paper, a proof is given that the Cointe–van Daalen's and the Tanizawa–Berkvens’ formulations are equivalent. It leads to a simplified version of Cointe–van Daalen's formulation. The formulation is validated against the analytical solution for a moving sphere in an unbounded water domain. |
| Keywords: | Potential flow Time domain Freely-floating body Time derivative of velocity potential Body boundary condition |
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