Nonlinear free surface potential flow simulations for hulls with a transom stern operating in dry and wet conditions

We present the results of a reduced model for the simulation of three dimensional unsteady nonlinear water waves. The model, designed to evaluate the wave drag of arbitrarily shaped ship hulls, is based on the potential flow theory. The governing Laplace equation is complemented by non penetration boundary conditions on the hull, and with fully nonlinear boundary conditions on the water free surface. The spatial discretization of the resulting time dependent boundary value problem is carried out by means of a collocated and iso-parametric Boundary Element Method (BEM) implemented making use of the open source library deal.II. The time integration of the nonlinear differential-algebraic system resulting from the spatial discretization is performed by means of an implicit Backward Differentiation Formula (BDF) method implemented in the open source library. The classes of the OpenCASCADE library have been used to interface the model with CAD data structures. The model also accounts for hulls with a transom stern. In such case, a specific treatment of the free surface nodes on the stern edge has been implemented. At low speeds, when the transom stern is partially immersed, a pressure patch is applied on the water surface detaching from the transom stern, to recover the gravity effect of the recirculating water on the underlying irrotational flow domain. The pressure patch is computed making use of experimental correlations obtained by Doctors et al. The test cases considered are that of the the US Navy Combatant DTMB-5415 and the National Physical Laboratory (NPL) hull. Numerical results are compared with experimental data.