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Numerical Analysis of Second-Order Mean Wave Forces by a Stabilized Higher Order Boundary Element Method

[+] Author Affiliations
Yan-Lin Shao

Technical University of Denmark, Lyngby, Denmark

Paper No. OMAE2018-78350, pp. V009T13A019; 10 pages
doi:10.1115/OMAE2018-78350
From:
  • ASME 2018 37th International Conference on Ocean, Offshore and Arctic Engineering
  • Volume 9: Offshore Geotechnics; Honoring Symposium for Professor Bernard Molin on Marine and Offshore Hydrodynamics
  • Madrid, Spain, June 17–22, 2018
  • Conference Sponsors: Ocean, Offshore and Arctic Engineering Division
  • ISBN: 978-0-7918-5130-2
  • Copyright © 2018 by ASME

abstract

A stabilized Higher-Order Boundary Element Method (HOBEM) based on cubic shape functions is presented to solve the linear wave-structure interaction with the presence of steady or slowly varying velocities. The m-terms which involves second derivatives of local steady flow are difficult to calculate accurately on structure surfaces with high curvatures. They are also not integrable at the sharp corners. A formulation of the Boundary Value Problem (BVP) in a body-fixed coordinate system is thus adopted, which avoids the calculation of the m-terms. The use of body-fixed coordinate system also avoid the inconsistency in the traditional perturbation method when 2nd order slowly-vary motions are larger than the linear motions.

The stabilized numerical method presented in this paper is based on streamline integration and biased differencing scheme along the streamlines. The presence of convective terms in the kinematic and dynamic free surface conditions will lead to instable solution if the explicit method is used. Thus a fully implicit scheme is used in this paper for the time integration of kinematic and dynamic free surface conditions. In an implicit scheme, solution of an additional matrix equation is normally required due to the fact that the presence of convective terms are approximated using the variables at current time step rather than the previous time steps only. A method that avoids solving such matrix equation is presented in this paper, which will reduce the computational efforts in the implicit method. The methodology is applicable on unstructured meshes. It can also be used in general second order wave-structure interaction analysis with presence of steady or slowly-varying velocities.

Copyright © 2018 by ASME

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