A B-Spline Rankine Panel Method for the Double-Body Flow Problem Solution for Time Domain Seakeeping Applications

A computationally efficient three-dimensional B-Spline Rankine Panel Method (B-RPM), tailored for solving the double-body flow problem in marine hydrodynamics and seakeeping scenarios with a free surface, is presented. The double-body flow, which is the main and time-independent contribution, serves as the basis flow for the overall hydrodynamic problem for time domain ship motions, ruled by the Laplace equation. Initially, a technique was developed that employed constant source distributions to solve the double-body flow. In a subsequent phase, the method is enhanced for problems involving hydrodynamic circulation by incorporating B-Spline sources and normal dipoles distributions on both body and free surfaces. An integral approach has been devised, leveraging the second Green identity and constant sources distribution to address double-body flow and evaluate potential second derivatives on the free surface, respectively. While focused on simple geometries for initial simulations and validation, this work marks the first stage of a broader time-domain model. The findings demonstrate that the B-RPM enables achieving comparable results with fewer panels than traditional constant source distribution methods. Additionally, it makes the direct analytical calculation of potential derivatives possible.