Use of body-fixed coordinate system in analysis of weakly nonlinear wave-body problems

Yanlin Shao, Odd M. Faltinsen

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

When a weakly nonlinear wave-body problem is considered in an inertial coordinate system, high-order derivatives appear in the higher-order body boundary conditions and make it difficult to get convergent and accurate results, especially for bodies with sharp corners or high surface curvatures. In this paper, a new method taking the advantage of the accelerated body-fixed coordinate system is proposed to avoid derivatives of the velocity potential on the right-hand side of the body boundary conditions. A domain decomposition method is applied with the use of the body-fixed coordinate system in the inner domain and the Earth-fixed coordinate system in the outer domain. The second-order radiation and diffraction of bodies with and without sharp corner are studied in the time domain and verified. A numerical beach is applied. Unlike the other methods which transfer the high-order derivatives to lower-order ones by using Stokes-like theorems, it is straightforward to generalize the present method to higher than second-order radiation problems and to the nonlinear wave-body analysis when the forward speed or current is included. (C) 2010 Elsevier Ltd. All rights reserved.
Original languageEnglish
JournalApplied Ocean Research
Volume32
Issue number1
Pages (from-to)20-33
ISSN0141-1187
DOIs
Publication statusPublished - 2010
Externally publishedYes

Keywords

  • Body-fixed coordinate system
  • Weakly nonlinear
  • Wave-body problem
  • Sharp corner

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