Development of time-domain Rankine source method for multiple floating bodies with large plane displacement

Abstract

In this study, we developed a numerical code utilizing the indirect boundary integral equation method (IBIEM) to analyze the hydrodynamics of multiple floating bodies undergoing large plane displacement. Conventional methods, which apply boundary conditions at a mean position, fall short in accounting for hydrodynamic interactions arising from these large relative displacements. To address this, our approach involves updating the boundaries of both the free surface and floating bodies, necessitating boundary reconstruction and interpolation techniques. To streamline the boundary reconstruction process, we introduced a desingularization strategy for the panel elements of the free surface. This allows for the simplification of node relocation instead of remeshing. We also developed an optimal node relocation algorithm, leveraging interbubble forces to appropriately reposition the nodes on the free surface. To interpolate the physical quantities associated with the newly scattered nodes on the free surface, we employed a thin-plate spline interpolation method. We then applied the newly developed numerical code to various hydrodynamic problems, using numerical computation for validation. Our results closely align with those obtained from reference model tests. Notably, our code successfully captures the actual phenomenon, such as modulation and the Doppler effect due to large displacement, which conventional methods fail to capture.