Numerical dispersion and damping on steady waves with forward speed

This paper examines the effects of numerical dispersion and damping associated with the Rankine panel method. In particular, the extent to which desingularization and collocation point shift alter these effects in both deep and shallow water is studied. A theoretical formulation predicts the trends in these effects, and these are validated numerically. While the use of constant singularity panels is found to shorten wavelengths, and upstream shifting of collocation-points results in numerical damping, the use of desingularization is found to temper both of these effects. An additional consequence of desingularization in finite depth problems is shown as an effective deepening of the fluid depth. An error index is proposed, for use in determining the optimal parameters for the Rankine panel scheme to be used.