Volume 22, Number 1, January-March 2016
|Page(s)||88 - 111|
|Published online||23 November 2015|
A theoretical and numerical determination of optimal ship forms based on Michell’s wave resistance
Universitéde Poitiers, Laboratoire de Mathématiques et
Applications UMR CNRS 7348, Téléport 2 – BP 30179, Boulevard Marie et Pierre Curie, 86962
2 Institut Pprime UPR 3346, Département Fluides, Thermique, Combustion, CNRS – Université de Poitiers – ENSMA, SP2MI – Téléport 2, 11 Boulevard Marie et Pierre Curie, BP 30179, 86962 Futuroscope Chasseneuil cedex, France
We determine the parametric hull of a given volume which minimizes the total water resistance for a given speed of the ship. The total resistance is the sum of Michell’s wave resistance and of the viscous resistance, approximated by assuming a constant viscous drag coefficient. We prove that the optimized hull exists, is unique, symmetric, smooth and that it depends continuously on the speed. Numerical simulations show the efficiency of the approach, and complete the theoretical results.
Mathematics Subject Classification: 49J20 / 76B75 / 76M30
Key words: Quadratic programming / obstacle problem / Sobolev space / Uzawa algorithm / parametric shape optimization
© EDP Sciences, SMAI 2015
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