The motivation for developing a new numerical code to predict wave resistance of conventional ships is that current numerical codes do not predict the wave resistance satisfactorily, especially in the design stage when evaluating different concepts with small differences in the geometries.

We are looking for a numerical method that is robust and easy for an engineer to use. For the wave resistance problem it is believed that the strong nonlinear effects are only located in the bow region. Then one can use non-linear methods to predict additional nonlinear contribution at the bow region. The method means that one use two-dimensional Laplace equation and three-dimensional free-surface conditions. A numerical program WAVERES is developed as part of the strategic research program SKIPRO 2001 at MARINTEK.

Verifications and Validation

The numerical program of the linear 3D solution has been verified by comparing with analytical and semi-analytical solutions. The first case is the flow past a sphere in infinite fluid. Both the velocity potential and the velocity on the body surface are checked. Satisfactory agreement is obtained. The second case is to test the numerical solution against the Green’s function (source) with forward speed. Good agreement is obtained. The method has been verified by thin ship theory for the wave resistance of the Wigley hull. Good agreement between the numerical and analytical solutions is obtained. The theory has been validated by model tests for a number of passenger ships and car ferries, which have been carried out at MARINTEK.

The example below shows the experimental and numerically calculated residuary resistance coefficients of a model with and without bulb. The residuary resistance is significantly reduced for the model with bulb both in the experimental and theoretical results. The numerical results agree well with experimental results. It should also be noted that WAVERES predicts the residual resistance significantly better than the commercial CFD program Shipflow.

Input and Output

The program WAVERES is an MS-DOS based program. Thus, it can run directly under MS-DOS using a DOS extender, or it can run in a DOS-windows under Windows 95/98/NT. WAVERES uses modules from ShipShape to import hull geometry and generate elements on the body and free surface. NAPA and several other formats can be imported. In addition, there are capabilities for interactive input and editing of the hull lines. When the hull lines are successfully entered in the program, the program will generate elements on the body and the free surface. The other data needed from the user are the mean draught, trim and forward speeds of the ship. The input windows and a view of the resulting elements on the body are shown in the screenshots on this page.


(You can see larger version of these two figures by clicking on them.)

Results from the program are the resistance of ship, sinkage and trim, wave elevation, pressure distribution on the hull and the velocity field everywhere in the fluid. An example of the wave elevation around the ship is given by a color print.

PDF-file of WAVERES presentation

Contact person at MARINTEK: Rong Zhao

Published February 21, 2005