B-Spline Approximation of Ship Waves on the Free Surface
ABSTRACT
We consider the problem of a ship advancing in waves. In this method, the zone of free surface in the vicinity of body is discretized. On the discretized surface, the first-order and second-order derivatives of ship waves are represented by the B-Spline formulae. Different ship waves are approximated by cubic B-spline and the first and second order derivates of incident waves are calculated and compared with analytical value. It approves that this numerical method has sufficient accuracy and can be also applied to approximate the velocity potential on the free surface.
Cite this paper
Li, F. , Li, H. and Ren, H. (2015) B-Spline Approximation of Ship Waves on the Free Surface. Journal of Applied Mathematics and Physics, 3, 81-85. doi: 10.4236/jamp.2015.31011.
Li, F. , Li, H. and Ren, H. (2015) B-Spline Approximation of Ship Waves on the Free Surface. Journal of Applied Mathematics and Physics, 3, 81-85. doi: 10.4236/jamp.2015.31011.
References
[1] Gordon, W.J. and Riesenfeld, R.F. B-Spline Curves and Surfaces [A]. [2] De Boor, C. (1972) On Calculation with B-Splines. J. Approx. Theory. [3] Hoschek, J. and Lasser, D. (1993) Fundamentals of Computer Aided Geometric Design. A K Peters. [4] Farin, G. (1993) Curves and Surfaces for Computer Aided Geometric Design. Academic Press.
[1] Gordon, W.J. and Riesenfeld, R.F. B-Spline Curves and Surfaces [A]. [2] De Boor, C. (1972) On Calculation with B-Splines. J. Approx. Theory. [3] Hoschek, J. and Lasser, D. (1993) Fundamentals of Computer Aided Geometric Design. A K Peters. [4] Farin, G. (1993) Curves and Surfaces for Computer Aided Geometric Design. Academic Press.