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have the free-surface condition that can cope with the turbulent free-surface. Further researches must be focused on the development of novel modelling of nonlinear free-surface motions.

References

[1] Miyata, H. and Inui, T., ”Nonlinear ship waves,” Advances in Applied Mechanics, Vol. 24, 1984, pp. 215–288.

[2] Miyata, H., Inui, T. and Kajitani, H., ”Free surface shock waves around ships and their effects on ship resistance, ” Journal of The Society of Naval Architects of Japan, Vol. 147, 1981, pp. 1–9.

[3] Takahashi, M., Kajitani, H., Miyata, H. and Kanai, M., ”Characteristics of free surface shock waves around wedge models,” Journal of The Society of Naval Architects of Japan, Vol. 148, 1980, pp. 1–9.

[4] Longuet-Higgins, M.S. and Cokelet, D., ”The deformation of steep surface waves on water, I. A numerical method of computation,” Proceedings of the Royal Society of London, A.350, 1976, pp. 1–26.

[5] Hirt, C.W. and Nichols, B.D., ”Volume of fluid (VOF) method for the dynamics of free boundaries, ” Journal of Computational Physics, Vol. 39, 1981, pp. 201–225.

[6] Ng, C.O. and Kot, S.C., ”Computations of water impact on a two-dimensional flat-bottomed body with a volume-of fluid method,” Ocean Engineering, Vol. 19, No. 4, 1992, pp. 377–393.

[7] Miyata, H., ”Finite-difference simulation of breaking waves,” Journal of Computational Physics, Vol. 65, No. 1, 1986, pp. 179–214.

[8] Miyata, H. and Lee, Y.G., ”Vortex motions about a horizontal cylinder in waves,” Ocean Engineering, Vol. 17, No. 3, 1990, pp. 279–305.

[9] Miyata, H., Katsumata, M., Lee, Y.G. and Kajitani, H., ”A finite-difference simulation method for strongly interacting two-layer flow,” Journal of The Society of Naval Architects of Japan, Vol. 163, 1988, pp. 1–16.

[10] Xiao, F. and Yabe, T., ”A method to trace sharp interface of two fluids by one grid with density function,” Proceedings of the 5th International Symposium on Computational Fluid Dynamics, Vol. 3, 1993, pp. 337–342.

[11] Brackbill, Journal of U., Kothe, D.B. and Zemach, C., ”A continuum method for modeling surface tension,” Journal of Computational Physics, Vol. 100, 1992, pp. 335–354.

[12] Park, J.C. and Miyata, H., ”Numerical simulation of the nonlinear free-surface flow caused by breaking waves,” ASME, FED-Vol. 181, Free-Surface Turbulence, 1994, pp. 155–168.

[13] Kawamura, T. and Miyata, H., ”Simulation of nonlinear shipflows by density-function method,” Journal of The Society of Naval Architects of Japan, Vol. 176, 1994, pp. 1–10.

[14] Miyata, H. and Yamada, Y., ”A finite difference method for 3D flows about bodies of complex geometry in rectangular co-ordinate systems,” International Journal of Numerical Methods in Fluids, Vol. 14, 1992, pp. 1261– 1287.

[15] Miyata, H., Zhu, M. and Watanabe, O., ”Numerical study on a viscous flow with free-surface waves about a ship in steady straight course by a finite-volume method,” Journal of Ship Research, Vol. 36, No. 4, 1992, pp. 332– 345.

[16] Chan, R.O.C. and Street, R.L., ”A computer study of finite amplitude water waves,” Journal of Computational Physics, Vol. 6, 1970, pp. 68– 94.

[17] Park, J.C., Zhu, M. and Miyata, H., ”On the accuracy of numerical wave making techniques,” Journal of The Society of Naval Architects of Japan, Vol. 173, 1993, pp. 35–44.

[18] Miyata, H., Nishimura, S. and Masuko, A., ”Finite difference simulation of nonlinear waves generated by ships of arbitrary three-dimensional configuration,” Journal of Computational Physics, Vol. 60, No. 3, 1985, pp. 391– 436.

[19] Baba, E., ”A new compenent of viscous resistance,” Journal of The Society of Naval Architects of Japan, Vol. 125, 1969, pp. 23–34.

[20] Kanai, A. and Miyata, H., ”Elucidation of the structure of free surface shock waves about a wedge model by finite-difference method,” Journal of The Society of Naval Architects of Japan, Vol. 177, 1995, pp. 147–159(in Japanese).



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