  The paper is concerned with a node-based, gradient-driven, continuous adjoint
two-phase flow procedure to optimize the shapes of free-floating vessels and
discusses three topics. First, we aim to convey that elements of a
Cahn-Hilliard formulation should augment the frequently employed
Volume-of-Fluid two-phase flow model to maintain dual consistency. It is seen
that such consistency serves as the basis for a robust primal/adjoint coupling
in practical applications at huge Reynolds and Froude numbers. The second topic
covers different adjoint coupling strategies. A central aspect of the
application is the floating position, particularly the trim and the sinkage,
that interact with a variation of hydrodynamic loads induced by the shape
updates. Other topics addressed refer to the required level of density coupling
and a more straightforward -- yet non-frozen -- adjoint treatment of
turbulence. The third part discusses the computation of a descent direction
within a node-based environment. We will illustrate means to deform both the
volume mesh and the hull shape simultaneously and at the same time obey
technical constraints on the vessel's displacement and its extensions. The
Hilbert-space approach provides smooth shape updates using the established
coding infrastructure of a computational fluid dynamics algorithm and provides
access to managing additional technical constraints. Verification and
validation follow from a submerged 2D cylinder case. The application includes a
full-scale offshore supply vessel at Re=3E+08 and Fn=0.37. Results illustrate
that the fully parallel procedure can automatically reduce the drag of an
already pre-optimized shape by 9-13 within approximately O(10.000-30.000) CPUh
depending on the considered couplings and floatation aspects.
