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Journal of Engineering Mathematics

, Volume 71, Issue 4, pp 367–392 | Cite as

Practical mathematical representation of the flow due to a distribution of sources on a steadily advancing ship hull

  • Francis Noblesse
  • Gerard Delhommeau
  • Fuxin Huang
  • Chi Yang
Article

Abstract

A practical mathematical representation of the flow velocity due to a distribution of sources on the mean wetted hull surface and the mean waterline of a ship that steadily advances along a straight path in calm water, of large depth and lateral extent, is presented. A main feature of this flow representation is a simple analytical approximation—valid within the entire flow region—to the local flow component in the expression for the gradient of the Green function associated with the classical Kelvin–Michell linearized free-surface boundary condition. Another notable feature of the flow representation is that the singularity associated with the gradient of the Green function is removed, using a straightforward regularization technique. The flow representation only involves elementary continuous functions (algebraic, exponential and trigonometric) of real arguments. These functions can then be integrated using ordinary Gaussian quadrature rules. Thus, the flow representation is particularly simple and well suited for practical flow calculations. The specific case of a low-order panel method—in which the hull geometry, the source density, and the flow velocity are consistently represented via piecewise linear approximations within flat triangular hull panels or straight waterline segments—is considered.

Keywords

Free-surface flow Green function Source distribution Steady ship waves 

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Copyright information

© US Government 2011

Authors and Affiliations

  • Francis Noblesse
    • 1
  • Gerard Delhommeau
    • 2
  • Fuxin Huang
    • 3
  • Chi Yang
    • 3
  1. 1.David Taylor Model BasinNSWCCDWest BethesdaUSA
  2. 2.École Centrale de NantesCNRSNantesFrance
  3. 3.Department of Computational and Data SciencesGeorge Mason UniversityFairfaxUSA

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