On the development of a higher order time-domain Rankine panel method for linear and weakly non-linear seakeeping computations

  • Felipe Ruggeri
  • Rafael A. Watai
  • Claudio M. P. Sampaio
  • Alexandre N. Simos
Technical Paper


The development of a numerical method for the computation of the linear and weakly non-linear wave effects on floating bodies is presented. The method is formulated in terms of a higher order time-domain boundary elements method based on the Rankine sources. The higher order approach is assumed for both body geometry (using NURBS) and computed function (using B-splines), the former in a standard CAD geometry format to provide more flexibility. In this paper, the procedures adopted for the numerical solution of the main mathematical problems involved are thoroughly described and discussed, with the purpose of documenting important aspects of these methods that are often absent in the literature. Several verification cases are presented, including first-order quantities (motion RAOs, velocity field, and free-surface elevation) and second-order loads (mean drift, sum, and difference components). Regarding the latter, at the present stage of the development, the numerical method is able to compute the so-called quadratic components of forces and moments. For these loads, steady-state solutions in both monochromatic and bichromatic waves are compared to the results obtained with a well-known frequency-domain code.


Higher order boundary element method Time-domain Rankine sources Seakeeping Quadratic second-order loads. 



Felipe Ruggeri and Rafael Watai are thankful to the State of São Paulo Research Foundation, FAPESP, for providing their respective scholarship Grants (2012/06681-7) and (2010/08778-2). Alexandre Simos acknowledges the Brazilian National Research Council, CNPq, for his research grant. Authors are wish to thank Petrobras for supporting the previous work on the low-order TDRPM code, which actually motivated the present development.


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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2018

Authors and Affiliations

  1. 1.Numerical Offshore Tank (TPN)University of São PauloSão PauloBrazil

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