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Received August 7, 2001; Revised October 21, 2002; Accepted February 12, 2003Abstract. Automatic procedures for the design of ship hull geometries yielding minimal wave resistance andwave breaking are an attractive opportunity from both the economical and practical standpoints.59515
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Estimating thecost function gradient according to the Sensitivity Equation and Adjoint Methods (SEM, AM) instead of usingthe standard finite difference approximations has the potential of reducing the computational cost of the overalloptimization procedure. Aim of this paper is to assess the actual extent of the cost reduction. Speed-up factorsof up to 3.3 have been obtained in the evaluation of the cost function gradient and of about 1.6 in the overalloptimization procedure applied to an optimal shape design problem of an existing tanker ship. The SEM and AMmethods perform better than finite differences mainly because of (i) the smaller number of flow solutions neededto compute the cost function gradient and (ii) the opportunity of using the same LU factored matrix for both theflow solver and the SEM or AM equations, a circumstance arising as a consequence of having chosen a linearizedpotential flow model of the 3D free-surface problem.Keywords: sensitivity equation method, adjoint method, optimal shape design, numerical ship hydrodynamics1. IntroductionThe increased availability of low-cost computing power, coupled with the maturing ofnumerical techniques able to accurately predict the effects of body-flow interactions, havemade today the design of ship hull shapes with CFD tools affordable. The preliminarydefinition of the optimal hull shape by these methods is an attractive option from both theeconomical and practical standpoints, since it allows to reduce the total number of hullmodels required to be tested in towing tanks in order to complete the overall hydrodynamicdesign process of a ship, and to devise innovative hull shapes.Several criteria can be adopted to design optimal ship shapes, such as finding the shapeyielding minimal wave or total ship resistance, or a shape not generating breaking waves.Formany ships, wave resistancemay typically amount, depending on the ship’s speed, from10% up to 60% of the total resistance. A lower value of the wave resistance is associated with lower wave heights and with a reduction in breaking waves produced by the advancingship. Breaking waves also play a role in active and passive navy ship detection problems.Indeed, the hydrodynamic noise produced by the wave breaking can significantly reducethe efficiency of the ship detection equipment, usually located in the fore part of the ship,inside the bulb.1Breaking waves are also responsible for the possible detection of the shipby synthetic aperture radar (SAR) images of the sea surface. Furthermore, breaking wavesare always closely connected with vorticity and turbulence production at the free surface,as well as with air entrapment that leads to the formation of an intense bubbly flow in thewake of the ship, which poses again a significant signature threat.In the naval hydrodynamic context, non-interactive procedures have been recently pro-posed, aimed at finding an optimal ship hull by solving a nonlinear constrained optimizationproblem driven by flow field analyses obtained via CFD techniques. As an example, Taharaand Himeno (1998), Campana et al. (1999), Tahara et al. (2000), and Peri et al. (2001),use the standard Finite Difference technique (FD) to compute the gradient of the objectivefunction. In Campana et al. (1999) and Peri et al. (2001), sequential quadratic program-ming, nonlinear conjugate gradients and steepest descent strategies have been coupled withCFD solvers to deal with optimal design of a tanker. Effects of the Variable-fidelity (orVariable-complexity) modeling (Hutchison et al., 1994; Kaufman et al., 1996; Giunta et al.,1997; Alexandrov et al., 2000), on speeding up the optimization procedure have been alsoexplored, using a suite of grids of different refinement. A typical result of such analysesis shown in figure 1, where the original and the optimized fore part of a tanker ship aredrawn side by side so as to highlight the large change of the bow cross-sections requiredto significantly reduce the wave pattern generated by the ship advancement.