Development of an algorithm for the calculation of Froude-Krylov and diffraction forces using a multiparameter conformal mapping approach

One way to obtain the hydrodynamic forces over a ship (assuming a slender body) is to apply the Strip Theory, which consists in reducing a three-dimensional problem into a series of two-dimensional problems that are easier to solve. This transformation is possible by dividing the vessel into a finite number of sections of constant thickness, allowing the calculation of the forces and moments associated with each strip and integrate the results along the ship's length. The exciting forces acting on the vessel due to the waves are often divided into the Froude-Krylov and diffraction excitations. The Froude-Krylov forces represent the integration of the pressures applied on the hull of the ship because of the incident waves as if the ship was not present. The diffraction forces are caused by the presence of the ship diffracting the incident waves around it. The Froude-Krylov force can be calculated through direct integration of the known incident wave potential along the different sections of the hull. The diffraction excitation requires the determination of the velocity potential that can be studied using the multiparameter conformal mapping technique. This approach transforms the boundary of the submerged section of an arbitrary shape, of the ship under study, into a unitary semicircle form whose velocity potential solution already exists. So, in this work, by addressing symmetric naval hull cross-sections, we developed, tested, and discussed an algorithm using a multiparameter conformal mapping approach to find the Froude-Krylov and diffraction forces.