Development and Application of an inviscid Patch Method for Free-Surface Flows



Nearly all modern merchant ship hulls have a transom stern, which can be partially submerged under specific loading conditions. At low speed, a dead-water zone might form behind the transom. The dead-water zone is associated with pressure losses and significantly influences the wave pattern and resistance.

Potential-flow methods are associated with a short response time and moderate grid-generation efforts. Therefore they are still the most prominent hydrodynamic simulation tool in industrial ship design. For efficiency reasons they are also deemed to be appropriate for hull-form optimization.

An accurate and reliable prediction of resistance is crucial to the predictive success of a hull-shape design tool. Potential-flow methods are well established for the prognosis of the resistance and the wave pattern. Although they are intensively validated against model tests, the quality of the wave prediction behind the ship usually remains uncertain. The region aft of the ship is very seldom measured and also significantly affected by viscous effects, which can not be captured by potential-flow methods from frst principles.The present research effort is concerned with an improved resistance prediction for ships featuring wetted transom-stern flows using potential-flow methods.

The technical aims of the present effort are to assess and improve the respective resistance predictions. The related modifcations should not violate the simplicity of the approach and improve the treatment of wave pattern behind the ship – which in turn results in an improved resistance prediction.

Computational Method (pi-shallo)

The pi-shallo approach is based on boundary elements of 'patch '-type with point-source singularities, which offer a higher level of accuracy than other methods. Emphasis is given to steady state wave fields with free trim and sinkage also looking at the flow past transom sterns. Accordingly, a simple model to mimic viscous effects based on a dead-water model is included.

Examplary Applications

The first example refers to the predcited free-surface elevation for the well known Kriso container ship (KCS) at Fn= 0.26 using 1200 free-surface patches and 800 hull patches. Results are compared against experiments reported in the Gothenburg2000 workshop. The predicted residual resistance is slightly overpredicted (7%).


The second example refers to a container vessel computed with and without dead-water model. Left: top shows simulation without dead-water model, center shows experiments and bottom shows simulation with dead-water model; Right: comparison of residual resistance coefficients.


Project Duration



Dipl.-Ing. Ole Hympendahl
Prof. Dr.-Ing. Thomas Rung
cand. arch. nav. Johannes Will


The software has been developed under the aegis of the BMWi sponsored project ABSS (Akurate Berechnung der Strömung an einem Spiegelheck), which has been performed in colaboration with HSVA.

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