Geodesic
A theoretical and numerical determination of optimal ship forms based on Michell’s wave resistance
Dambrine, Julien1  ; Pierre, Morgan1  ; Rousseaux, Germain2 
1 Universitéde Poitiers, Laboratoire de Mathématiques et Applications UMR CNRS 7348, Téléport 2 – BP 30179, Boulevard Marie et Pierre Curie, 86962 Futuroscope Chasseneuil, France
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
ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 1, pp. 88-111

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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.

Reçu le :
DOI : 10.1051/cocv/2014067
Classification : 49J20, 76B75, 76M30
Keywords: Quadratic programming, obstacle problem, Sobolev space, Uzawa algorithm, parametric shape optimization

Dambrine, Julien 1 ; Pierre, Morgan 1 ; Rousseaux, Germain 2

1 Universitéde Poitiers, Laboratoire de Mathématiques et Applications UMR CNRS 7348, Téléport 2 – BP 30179, Boulevard Marie et Pierre Curie, 86962 Futuroscope Chasseneuil, France
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 
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     title = {A theoretical and numerical determination of optimal ship forms based on {Michell{\textquoteright}s} wave resistance},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {88--111},
     publisher = {EDP-Sciences},
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     year = {2016},
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Dambrine, Julien; Pierre, Morgan; Rousseaux, Germain. A theoretical and numerical determination of optimal ship forms based on Michell’s wave resistance. ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 1, pp. 88-111. doi: 10.1051/cocv/2014067

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