Finite difference method for 2-D and 3-D nonlinear free surface wave problems
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A finite difference method is developed for the numerical modelling of the 2-D and 3-D unsteady potential flow generated by transient disturbances on the free surface, on which the nonlinear boundary conditions are fully satisfied. The unknown function is computed with an iteration scheme processing in a transformed time-invariant space. After the velocity is calculated, the location of the free surface is renewed and so is the value of velocity on it. The boundary-value problem of the governing equation is then solved at the next time step. The present method incorporates the FFT. Consequently, a tri-diagonal equation system is obtained which could be readily solved. The feasibility of this method has been demonstrated by 2-D and 3-D examples corresponding to different initial disturbances.
Key Wordstransient flow nonlinear boundary conditions free surface wave fast Fourier transform (FFT) coordinate mapping iteration process
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- Harlow, F. H. and Welch, J. E.,Physics of Fluid,8, 12(1965), 218.Google Scholar
- Chan, R.K.-C. and Fromn, J. E., The digital simulation of water wave, Lecture Notes in Physics, 8, Springer-Verlag, Berlin, 1(1970), 429.Google Scholar
- Taylor, C. J., France, P. W. and Zienkiewicz, O. C., Some free surface transient flow problems of seepage and irrotational flow, The Mathematics of Finite Elements and Applications, Academic Press, N. Y., m 2(1973), 313.Google Scholar
- Visser W. and Van der Wilt, M., A numerical approach to the study of irregular ship motions, Finite Element Method in Flow Problems, UAH Press, Alabama (1974), 277.Google Scholar
- Bai, K. J., A localized finite element method for the uniform flow problems with a free surface, First International Conference on Numerical Ship Hydrodynamics, Gaithersburg, Maryland (1975), 209.Google Scholar
- Bai, K. J. and Yeung, R. W., Numerical solutions to free surface flow problems, Proceeding of the Tenth ONR Symposium on Naval Hydrodynamics, Cambridge, Mass. (1974), 609.Google Scholar
- Yen, S. M. and Lee, K. D., Application of finite element method to potential flow problems, Proceedings of the Second International Symposium on Finite Element Method to Potential Flow Problems, Rapallo, Italy (1976), 539.Google Scholar
- Haussling, H.J. and Van Eseltine, R. T., A combined spectral finite difference method for nonlinear water wave problems, Naval Ship R & D Center Report 4580 (1974).Google Scholar
- Haussling, H. J. and Van Eseltine, R. T., Finite difference method for transient potential flows with free surface, First International Conference on Numerical Ship Hydrodynamics, Gaithersburg, Maryland (1975), 295.Google Scholar