An efficient shape parametrisation by free-form deformation enhanced by active subspace for hull hydrodynamic ship design problems in open source environment

In this contribution, we present the results of the application of a parameter space reduction methodology based on active subspaces property to the hull hydrodynamic design problem. In the framework of such typical naval architecture problem, several parametric deformations of an initial hull shape are considered to assess the influence of the shape parameters considered on the hull total drag. The hull resistance, which is the performance parameter associated with each parametric hull, is typically computed by means of numerical simulations of the hydrodynamic flow past the ship. Such problem is extremely relevant at the preliminary stages of the ship design, when several flow simulations are typically carried out by the engineers to establish a certain sensibility on the total drag dependence on the hull geometrical parameters considered and on other physical parameters. Given the high number of geometric and physical parameters involved which might result in a high number of time consuming hydrodynamic simulations assessing whether the parameters space can be reduced would lead to considerable computational cost reduction at the design stage. Thus, the main idea of this work is to employ the active subspaces to identify possible lower dimensional structures in the parameter space, or to verify the parameter distribution in the position of the control points. To this end, a fully automated procedure has been implemented to produce several small shape perturbations of an original hull CAD geometry which are then used to carry out high-fidelity flow simulations in different cruise conditions and collect data for the active subspaces analysis. To achieve full automation of the open source pipeline described, both the free form deformation methodology employed for the hull perturbations and the high fidelity solver based on unsteady potential flow theory, with fully nonlinear free surface treatment, are directly interfaced with CAD data structures and operate using IGES vendor-neutral file formats as input files. The computational cost of the fluid dynamic simulations is further reduced through the application of dynamic mode decomposition to reconstruct the final, steady state total drag value given only few initial snapshots of the simulation. The active subspaces analysis is here applied to the geometry of the DTMB-5415 naval combatant hull, which is a common benchmark in ship hydrodynamics simulations, within the SISSA mathLab applied mathematics lab. The contribution will discuss several details of the implementation of the tools developed, as well as the results of their application to the target engineering problem.