Enhanced Endo’s approach for evaluating free-surface Green’s function with application to wave-structure interactions

Bayati, I., Gueydon, S., Belloli, M., 2015. Study of the effect of water depth on potential flow solution of the

OC4 semisubmersible floating offshore wind turbine. Energy Procedia 80, 168-176.

Benitz, M.A., Schmidt, D.P., Lackner, M.A., Stewart, G.M., Jonkman, J.M., Robertson, A., 2015. Validation

of hydrodynamic load models using CFD for the OC4-DeepCwind semisubmersible. In: Proceedings of the

ASME 2015 34th International Conference on Ocean, Offshore and Arctic Engineering. St. John’s, NL,

Canada.

Chakrabarti, S.K., 2001. Application and verification of deepwater Green function for water waves. Journal

of Ship Research 45, 187-196.

Chen, X.B., 1993. Evaluation de la fonction de Green du probleme de diffraction/radiation en profondeur

d’eau finie-une nouvelle méthode rapide et précise, Actes des 4e Journées de l’Hydrodynamique, Nantes

(France), 371–384.

Chen, X.B., 2004. Hydrodynamics in offshore and naval applications - Part I. In: Proc. Of the 6th Intl. Conf.

Hydrodynamics, Perth, Australia.

Clément, A., 2013. A second order ordinary differential equation for the frequency domain Green function,

in: Proceedings of 28th International Workshop on Water Waves and Floating Bodies, Marseille, France.

Endo, H., 1983. Numerical evaluation of principal value integral by Gauss-Laguerre quadrature. AIAA

Journal 21,149-151.

Endo, H., 1987. Shallow-water effect on the motions of three-dimensional bodies in waves. Journal of ship

research 31, 34-40.

John, F., 1950. On the motion of floating bodies II. Communications on Pure and Applied Mathematics 3, 45101.

Li, L., 2001. Numerical seakeeping predictions of shallow water effect on two ship interactions in waves. Ph.

D. thesis. Dalhousie University, Halifax, Canada.

Liang, H., Wu, H., Noblesse, F., 2018. Validation of a global approximation for wave diffraction-radiation in

deep water. Applied Ocean Research 74, 80–86.

Linton, C.M., 1999. Rapidly convergent representations for Green functions for Laplace's equation.

Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences 455, 1767-1797.

29

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

Liu, R., Ren, H., Li, H., 2008. An improved Gauss–Laguerre method for finite water depth Green function

and its derivatives. Journal of Ship Mechanics 12, 188–196.

Liu, Y., Iwashita, H., Hu, C., 2015. A calculation method for finite depth free-surface green function.

International Journal of Naval Architecture and Ocean Engineering 7, 375-389.

Liu, Y., Hu, C., Sueyoshi, M., Iwashita, H., Kashiwagi, M., 2016. Motion response prediction by hybrid

panel-stick models for a semi-submersible with bracings. Journal of Marine Science and Technology 21, 742757.

Liu, Y., Yoshida, S., Hu, C., Sueyoshi, M., Sun, L., Gao, J., Cong, P., He, G., 2018a. A reliable open-source

package for performance evaluation of floating renewable energy systems in coastal and offshore regions.

Energy Conversion and Management 174, 516-536.

Liu, Y., Yoshida, S., Yamamoto, H., Toyofuku, A., He, G., Yang, S., 2018b. Response Characteristics of the

DeepCwind Floating Wind Turbine Moored by a Single-Point Mooring System. Applied Sciences 8, 2306.

Liu, Y., 2019. HAMS: A Frequency-Domain Preprocessor for Wave-Structure Interactions—Theory,

Development, and Application. Journal of Marine Science and Engineering 7, 81.

Mei, C.C., Stiassnie, M., Yue, D.K.P., 2005. Theory and applications of ocean surface waves: nonlinear

aspects. World scientific.

Newman, J.N., 1985. Algorithms for free-surface Green function. Journal of Engineering Mathematics 19,

57-67.

Newman, J.N., 1986. Distributions of sources and normal dipoles over a quadrilateral panel. Journal of

Engineering Mathematics 20, 113-126.

Newman, J.N., 1990. Numerical solutions of the water-wave dispersion relation. Applied Ocean Research 12,

14-18.

Newman, J.N., 1992. The approximation of free-surface Green functions. Retirement Meeting for Professor

Fritz Ursell, University of Manchester, published in “Wave Asymptotics” edited by Martin PA and Wickham

GR, pp. 107-135. Cambridge University Press.

Noblesse, F., 1982. The Green function in the theory of radiation and diffraction of regular water waves by a

body. Journal of Engineering Mathematics 16, 137–169.

Peter, M.A., Meylan, M.H., 2004. The eigenfunction expansion of the infinite depth free surface Green

function in three dimensions. Wave Motion 40, 1–11.

Pidcock, M.K., 1985. The calculation of Green functions in three dimensional hydrodynamic gravity wave

problems. International Journal for Numerical Methods in Fluids 5, 891-909.

Ponizy, B., Noblesse, F., Ba, M., Guilbaud, M., 1994. Numerical evaluation of free-surface Green function.

Journal of Ship Research 38, 193–202.

Press, W.H., Flannery, B.P., Teukolsky, S.A., Vetterling, W.T., 2007. Numerical Recipes: The Art of

Scientific Computing (3rd ed.). Cambridge University Press.

Robertson, A., Jonkman, J.M., Masciola, M., Song, H., Goupee, A., Coulling, A., Luan, C., 2014. Definition

of the Semisubmersible Floating System for Phase II of OC4. National Renewable Energy Laboratory

(NREL), Golden, CO. Technical Report No NREL/TP-5000-60601.

30

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

Shan, P.H., Wu, J.M., 2018. Highly precise approximation of free surface Green function and its high order

derivatives based on refined subdomains. Brodogradnja/Shipbuilding 69, 53–70.

Shan, P., Zhu, R., Wang, F., Wu, J., 2019. Efficient approximation of free-surface Green function and

OpenMP parallelization in frequency-domain wave–body interactions. Journal of Marine Science and

Technology 24, 479-489.

Sun, L., Teng, B., Liu, C.F., 2008. Removing irregular frequencies by a partial discontinuous higher order

boundary element method. Ocean Engineering 35, 920-930.

Telste, J.G., Noblesse, F., 1986. Numerical evaluation of the Green function of water-wave radiation and

diffraction. Journal of Ship Research 30, 69-84.

Wikipedia

(accessed

on

Feb.

https://en.wikipedia.org/wiki/Gauss%E2%80%93Laguerre_quadrature

16,

2020):

Wu, H., Zhang, C., Zhu, Y., Li, W., Wan, D., Noblesse, F., 2017. A global approximation to the Green

function for diffraction radiation of water waves. European Journal of Mechanics-B/Fluids 65, 54-64.

Wu, H., Liang, H., Noblesse, F., 2018. Wave component in the Green function for diffraction radiation of

regular water waves. Applied Ocean Research 81, 72-75.

Xie, C., Choi, Y., Rongère, F., Clément, A.H., Delhommeau, G., Babarit, A., 2018. Comparison of existing

methods for the calculation of the infinite water depth free-surface Green function for the wave–structure

interaction problem. Applied Ocean Research 81, 150-163.

Zhang, S., Jin, J.M., 1996. Computation of special functions. Wiley-Interscience.

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