Adjoint node-based shape optimization of free-floating vessels

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 = 3 × 10 8 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 ≈O(10,000-30,000) CPUh depending on the considered couplings and floatation aspects.