Adjoint Multiphase Optimisation of Ships with high Wave Resistance

Numerische Optimierung von Schiffen mit hohem Wellenwiderstand (NoWelle)


The project is concerned with the derivation of an adjoint complement to two-phase flow finite-volume procedures dedicated to shape optimisations in marine engineering flows.

The strategy refers to an extension of a hybrid continuous/discrete adjoint method for

two-phase flow Volume-of-Fluid (VoF) approaches which are of particular relevance due to their widespread industrial usage.


The results refer to an accurate and stable adjoint VoF-scheme derived from an analysis of the individual adjoint coupling terms which originate from phase field related variations of density and viscosity. As a measure for accuracy, the adjoint consistency is verified against  results of a direct differentiation technique for a benchmark flows. Moreover merchant vessels are optimised for a number of objective functions.  

The project also aims to outline means to efficiently employ standard geometry constraints (e.g. max. length, width, draft, flat of bottom or flat stern areas), as well as strategies to filter deformations on a tensorial bases to transform computed shape derivatives into shape gradients and thus allow for extrem shape changes in conjunction with a CAD-free, mesh-morphing approach. 



Comparison of frames of the initial (black) and the optimised (orange) configuration for a container vessel. Resulting drag improved about 8% at Fn=0.26 due to a separation of the bow and shoulder wave systems and an increased wetting of the stern.



Project Duration



Dipl.-Ing. Jörn Kröger
Prof. Dr.-Ing. Thomas Rung

Industrial Partners

Hamburgische Schiffbau-Versuchsanstalt, Friendship Systems, VOITH