Robust optimal ship hulls based on Michell's wave resistance

Abstract

We seek the hull of a ship with a given volume which minimizes the water resistance with uncertainties on the cruising speed. The water resistance is based on Michell's wave resistance functional, and the speed is a random variable whose probability distribution is known. We first handle the case where the support of the hull is given and then we also optimize this support for a given area. In each case, an optimal hull is shown to exist. The numerical simulations are costly so we adapt to our problem Newton's method for shape optimization. The Dirichlet energy is used as a test case. The numerical results for the robust optimal hull are compared with the case where the cruising speed is known.