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Numerical method in wave-body interactions

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Abstract

The application of Green's function in calculation of flow characteristics around submerged and floating bodies due to a regular wave is presented. It is assumed that the fluid is homogeneous, inviscid and incompressible, the flow is irrotational and all body motions are small. Two methods based on the boundary integral equation method (BIEM) are applied to solve associated problems. The first is a low order panel method with triangular flat patches and uniform distribution of velocity potential on each panel. The second method is a high order panel method in which the kernels of the integral equations are modified to make it nonsingular and amenable to solution by the Gaussian quadrature formula. The calculations are performed on a submerged sphere and some floating spheroids of different aspect ratios. The excellent level of agreement with the analytical solutions shows that the second method is more accurate and reliable.

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References

  1. 1.

    C. A. Brebbia,The boundary element method for engineers Pentech Press, London, 1984.

  2. 2.

    O. M. Faltinsen and F. C. Michelson,Motion of large structures in waves at zero Froude number, Proc. Dynamics of Marine Vehicles and Structures in Waves, London, (1974), 99–114.

  3. 3.

    C. J. Garrison,Hydrodynamic loading of large volume offshore structures: Three dimensional source distribution methods, Numerical Methods in Offshore Engineering, ed. O. C. Zienkiewicz et al. Wiley, Chichester, (1979), 87–140.

  4. 4.

    J. L. Hess and A. M. O. Smith,Calculation of nonlifting potential flow about arbitrary three-dimensional bodies, Journal of Ship Research8 (Sept. 1964), 22–44.

  5. 5.

    A. Hulme,The wave forces acting on a floating hemisphere undergoing forced periodic oscillations, J. Fluid Mech.121 (1982), 443–463.

  6. 6.

    R. B. Inglis and W. G. Price,Comparison of calculated responses for arbitrary shaped bodies using two-and three dimensional theories, Int. Shipbuilding Progress27 (Jan. 1980), 86–95.

  7. 7.

    L. Landweber and M. Macagno,Irrotational flow about ship forms, IIHR Report No. 123, Iowa Institute of Hydraulic Research, The University of Iowa, Iowa City, Iowa, 1969.

  8. 8.

    J. G. Telste and F. Noblesse,Numerical evaluation of the Green function of water-wave radiation and diffraction, Journal of Ship Research30 (June 1986), No. 8, 69–84.

  9. 9.

    J. N. Newman,Double-precision evaluation of the oscillatory source potential, Journal of Ship Research28(3) (Sept. 1984), 151–154.

  10. 10.

    J. N. Newman and C. H. Lee,Boundary-element method in offshore structure analysis, Journal of Offshore Mech. and Arctic Eng.124 (May 2002), 81–89.

  11. 11.

    M. Rahman,Effect of diffraction and radiation on a submerged sphere, IJMMS,28:9 (2001), 499–515.

  12. 12.

    W. C. Webster,The flow about arbitrary, three-dimensional smooth bodies, Journal of Ship Research19(4) (Dec. 1975), 206–218.

  13. 13.

    J. V. Wehausen and E. V. Laitone,Surface waves, Encyclopedia of physics, Fluid dynamics 3, Springer-Verlag, Berlin4 (1960).

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Author information

Correspondence to M. Rahman.

Additional information

Professor Matiur Rahman is a faculty member of Dalhousie University in Halifax, Canada. Originally from the foothills of the Himalalayas in the state of Assam, in India, he received PhD (1973) from Winsor University, Canada and his DSc(Eng) (1992) from London University, UK. His other academic achievements include a BSc (Hons) (1962) from Cotton College, India; an MSc (1964) from Gauhati University, India; DIC (1969) from Imperial College, UK and a MPhil (1969) from London University, UK. Professor Rahman has published 15 textbooks and research monographs and over 200 research papers in refereed journals and proceedings. Professor Rahman's main research interests are in areas of waves and hydrodynamics loading, fluid-structure interaction, natural convection flows with diffusion and reaction, stability of tubular chemical flow reactors, temperature stratification in large bodies of water, and non-linear ocean waves.

S. Hossein Mousavizadegan received his BS from Iran University of Science and Technology in 1985 in Mechanical Engineering, and his MSc. from Technical University of Gdansk in Poland in Naval Architecture in 1993. He was at Amirkabir University of Technology in Tehran, in Iran, as instructor from 1993 to 2000. He started his PhD program in September 2000 in Mechanical Engineering Department of Dalhousie University in Canada in the field of the Marine Hydrodynamics. He has already published more than five papers during his PhD study. His research area is in the computational methods in wave-body interactions.

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Mousavizadegan, S.H., Rahman, M. Numerical method in wave-body interactions. JAMC 17, 73–91 (2005). https://doi.org/10.1007/BF02936042

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AMS Mathematics Subject Classification

  • 76B07
  • 76M15

Key words and phrases

  • Potential flow
  • Green's function
  • singularity
  • panel method
  • radiation
  • diffraction