Numerical Aspects of the Neumann-Kelvin Problem

The Neumann-Kelvin problem for a surface ship traveling at a steady speed represents an approximate solution to the inviscid flow, and is subjected to a range of numerical experiments in the present paper. The solution is obtained by replacing the ship by a surface source distribution. The hull is discretized into a set of flat panels in the numerical procedure. The main difficulty is the accurate calculation of the influence of the various panels on each other. Most previous workers have replaced the wave portion of the potential for each panel by an equivalent source at its centroid (the monopole method) in order to simplify this part of the calculations. In the present work, a technique of analytically integrating the panel source was used, so the above-mentioned approximation was eliminated. A comparison of the two methods shows that the monopole method appears to be less well behaved, in the limit, as the paneling of the hull surface is refined. However, for a course arrangement of panels, the results approximate those, of the consistent-panel technique. Numerical experiments were also performed on a submerged body. In this case, the monopole method is valid, and can be used to advantage to save computing effort.