| Abstract: | An analysis is given for the accuracy and stability of some perturbation‐based time‐domain boundary element models (BEMs) with B‐spline basis functions, solving hydrodynamic free‐surface problems, including forward speed effects. The spatial convergence rate is found as a function of the order of the B‐spline basis. It is shown that for all the models examined the mixed implicit–explicit Euler time integration scheme is correct to second order. Stability diagrams are found for models based on B‐splines of orders third through to sixth for two different time integration schemes. The stability analysis can be regarded as an extension of the analysis by Vada and Nakos Vada T, Nakos DE. Time marching schemes for ship motion simulations. In Proceedings of the 8th International Workshop on Water Waves and Floating Bodies, St. John's, Newfoundland, Canada, 1993; 155–158] to include B‐splines of orders higher than three (piecewise quadratic polynomials) and to include finite water depth and a current at an oblique angle to the model grid. Copyright © 2000 John Wiley & Sons, Ltd. |
