A theoretical and numerical determination of optimal ship forms based on Michell’s wave resistance

Dambrine, Julien; Pierre, Morgan; Rousseaux, Germain

ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 1, pp. 88-111.

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.

Classification : 49J20, 76B75, 76M30
Mots clés : Quadratic programming, obstacle problem, Sobolev space, Uzawa algorithm, parametric shape optimization

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