Application of method of fundamental solutions in solving potential flow problems for ship motion prediction

A novel panel-free approach based on the method of fundamental solutions (MFS) is proposed to solve the potential flow for predicting ship motion responses in the frequency domain according to strip theory. Compared with the conventional boundary element method (BEM), MFS is a desingularized, panel-free and integration-free approach. As a result, it is mathematically simple and easy for programming. The velocity potential is described by radial basis function (RBF) approximations and any degree of continuity of the velocity potential gradient can be obtained. Desingularization is achieved through collating singularities on a pseudo boundary outside the real fluid domain. Practical implementation and numerical characteristics of the MFS for solving the potential flow problem concerning ship hydrodynamics are elaborated through the computation of a 2D rectangular section. Then, the current method is further integrated with frequency domain strip theory to predict the heave and pitch responses of a containership and a very large crude carrier (VLCC) in regular head waves. The results of both ships agree well with the 3D frequency domain panel method and experimental data. Thus, the correctness and usefulness of the proposed approach are proved. We hope that this paper will serve as a motivation for other researchers to apply the MFS to various challenging problems in the field of ship hydrodynamics.