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12. Jensen, G.; Söding, H., “Ship wave-resistance computations”, Notes on Num. Fluid Mech. Vol. 25: “Finite approximations in fluid mechanics”, Springer, Berlin, Heidelberg, New York, Tokyo, 1989

13. Kajitani, H., “A wandering in some resistance components and flow”, Ship Techn. Res. 34/3, 1987, pp. 105–131



University of Michigan, USA

The patch method results are impressive. Is this improvement due primarily to moving the singularity distribution within the body or is the matching of the outflow through the patch also required? Specifically since (3) appears to ensure Σσi=O inside the closed body, is the extra effort in evaluating the trigonometric functions worth it?

Does the higher-order method you present make the patch method obsolete? Why would you still use the patch method?


The improvement in the patch method is not due to moving the singularities into the body, but due to “averaging” both the boundary condition and the results (e.g., the pressure) over each patch. Moving the singularity into the body would be helpful, but is possible only if the body surface is sufficiently smooth and if the body breadth is sufficient; these conditions are not satisfied at typical ships' ends. The extra effort for computing trigonometric functions appears only in comparison with a point-source-point-collocation method, which does not work well for typical ships; compared to a usual first-order panel method the numerical effort per panel/patch is about the same.

The higher-order method is more accurate for smooth bodies, but somewhat more complex to program. Comparisons for less smooth bodies like ships with sharp ends have not yet been made. Extension to free-surface flows may further change the rating.

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