Skip to main content
SpringerLink
Log in

Efficient approximation of free-surface Green function and OpenMP parallelization in frequency-domain wave–body interactions

  • Original article
  • Published:
Journal of Marine Science and Technology Aims and scope Submit manuscript

Abstract

The evaluation of Green function without translation has always been the most time-consuming part of the hydrodynamic analysis based on potential flow theory. This research investigates the new implementations of efficient approximations of Green function and the code parallelization with OpenMP library. First, algorithms of infinite-depth case are developed with economized Chebyshev polynomials based on modified region and subdomain partitions. Second, an improved Gauss–Laguerre method for the Cauchy integral is presented to evaluate the finite-depth case with the convergence acceleration by the reduction of fraction and singularity elimination by the infinite-depth case together with the exponential integral. For the analyzed container vessel, on the premise of good numerical accuracy, we conclude that the present method has nearly obtain the same efficiency as Chen (Hydrodynamics in offshore and naval applications—Part I, Bureau Veritas, Paris, 2004) for the infinite-depth case and almost 30% higher efficiency for the finite-depth case. Moreover, we also point out that the numerical efficiency is significantly enhanced again due to the OpenMP parallelization of the serial code.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. Noblesse F (1982) The Green function in the theory of radiation and diffraction of regular water waves by a body. J Engl Math 16:137–169

    Article  MathSciNet  MATH  Google Scholar 

  2. Wu HY, Zhang CL, Zhu Y, Li W, Wan DC, Noblesse F (2017) A global approximation to the Green function for diffraction radiation of water waves. Eur J Mech B Fluid 67:54–64

    Article  MathSciNet  MATH  Google Scholar 

  3. Newman JN (1985) Algorithms for free-surface Green function. J Eng Math 19(1):57–67

    Article  MATH  Google Scholar 

  4. Newman JN (1992) The approximation of free-surface Green functions. In: Martin PA, Wickham GR (eds) Retirement meeting for professor Fritz Ursell, University of Manchester, published in ‘Wave Asymptotics’, Cambridge University Press, Cambridge, pp 107–135

    Google Scholar 

  5. Chen XB (2004) Hydrodynamics in offshore and naval applications—part I. Bureau Veritas, Paris

    Google Scholar 

  6. Clement AH (2013) A second order ordinary differential equation for the frequency domain Green function. In: Proceedings 28th international workshop on water waves and floating bodies

  7. Shen Y, Yu DH, Duan WY, Li H (2016) Ordinary differential Equation algorithms for a frequency-domain water wave Green’s function. J Engl Math 100:53–66

    Article  MathSciNet  MATH  Google Scholar 

  8. Elia JD, Battaglia L, Storti M (2011) A semi-analytical computation of the Kelvin kernel for potential flows with a free surface. Comput Appl Math 30:267–287

    Article  MathSciNet  MATH  Google Scholar 

  9. Shan PH, Wu JM (2018) Highly precise approximation of free surface Green function and its high order derivatives based on refined subdomains. Brodogradnja/shipbuilding 69:53–70

    Google Scholar 

  10. Linton CM (1999) Rapidly convergent representations for Green functions for Laplace’s equation. Proc R Soc A Math Phys 455:1767–1797

    Article  MathSciNet  MATH  Google Scholar 

  11. Liu Y, Hidetsugu I, Hu CH (2015) A calculation method for finite depth free-surface green function. Int J Nav Archit Ocean Eng 7:375–389

    Article  Google Scholar 

  12. Li L (2001) Numerical seakeeping predictions of shallow water effect on two ship interactions in waves [D]. Ph. D. Dissertation. Dalhousie University

  13. Liu RM, Ren HL, Li H (2008) An improved Gauss–Laguerre method for finite water depth Green function and its derivatives. J Ship Mech 12:188–196

    Google Scholar 

  14. Chapman B, Jost G, Vander Pas R (2008) Using OpenMP: portable shared memory parallel programming, vol 10. MIT Press, Cambridge

    Google Scholar 

  15. Chandra R (2001) Parallel programming in OpenMP. Morgan Kaufmann, Massachusetts

    Google Scholar 

  16. Amritkar A, Deb S, Tafti D (2014) Efficient parallel CFD-DEM simulations using OpenMP. J Comput Phys 256:501–519

    Article  MathSciNet  MATH  Google Scholar 

  17. Sato Y, Hino T, Ohashi K (2013) Parallelization of an unstructured Navier–Stokes solver using a multi-color ordering method for OpenMP. Comput Fluids 88:496–509

    Article  MathSciNet  MATH  Google Scholar 

  18. Nishiura D, Furuichi M, Sakaguchi H (2015) Computational performance of a smoothed particle hydrodynamics simulation for shared-memory parallel computing. Comput Phys Commun 194:18–32

    Article  Google Scholar 

  19. Oh SE, Hong JW (2017) Parallelization of a finite element Fortran code using OpenMP library. Adv Eng Softw 104:28–37

    Article  Google Scholar 

  20. Dai YS (1998) Potential flow theory of ship motions in waves in frequency and time domain. The Express of the National Defense Industries, Beijing

    Google Scholar 

  21. Gil A, Segura J, Temme NM (2007) Numerical methods for special functions, the Society for Industrial and Applied Mathematics (SIAM), Philadelphia

  22. Mason JC, Handscomb D (2002) Chebyshev polynomials. CRC Press LLC, Florida

    Book  MATH  Google Scholar 

  23. Mei CC (1989) The applied dynamics of ocean surface waves (Advanced series on ocean engineering, vol 1. World Scientific, Singapore

    Google Scholar 

  24. Zhang J (2012). Investigation on coupling analysis between floating structure and flexible structure members [D]. Harbin Engineering University, Harbin

    Google Scholar 

Download references

Acknowledgements

This work has been financially supported by the MIIT High-Tech Ship Research Projects (Project No. [2016] 25-K24333).

Author information

Authors and Affiliations

  1. Marine Design and Research Institute of China, Shanghai, China

    Penghao Shan, Fuhua Wang & Jiameng Wu

  2. School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai, China

    Penghao Shan, Renchuan Zhu & Jiameng Wu

  3. Shanghai Key Laboratory of Ship Engineering, Shanghai, China

    Penghao Shan & Jiameng Wu

Authors
  1. Penghao Shan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Renchuan Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Fuhua Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jiameng Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Penghao Shan.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shan, P., Zhu, R., Wang, F. et al. Efficient approximation of free-surface Green function and OpenMP parallelization in frequency-domain wave–body interactions. J Mar Sci Technol 24, 479–489 (2019). https://doi.org/10.1007/s00773-018-0568-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00773-018-0568-9

Keywords

Search

Navigation