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.
Highlights
In the method for hydrodynamic analysis of floating bodies with forward speed, due to the complex boundary condition on the free surface, the integral equation involves the unknown velocity potential and its first-order and second-order derivatives on the free surface
We choose a set of points p i, j = (x, y, z) (i = 0,...,10, j = 0,...,41) on the free surface. (x, y) is position on the surface, z is the height of incident wave and it can be defined as Equation (9)
When the incident wave is given as z = 4 cos(0.0785x), the distribution of points p i, j (i = 0,...,10, j = 0,...,41) on the free surface is shown as Figure 1
Summary
In the method for hydrodynamic analysis of floating bodies with forward speed, due to the complex boundary condition on the free surface, the integral equation involves the unknown velocity potential and its first-order and second-order derivatives on the free surface. The incident wave on free surface is approximated by cubic B-spline and the relationship between incident wave and its first-order and second-order partial derivatives are derived and compared with the analytical value. This method is approved to have sufficient accuracy and can be applied to approximate the velocity potential on the free surface. We define the kth degree B-spline curve as Equation (1) [1]: How to cite this paper: Li, F., Li, H. and Ren, H.L. I=0 where d i is control vertices, n + 1 is the number of control vertices, Ni,k (u) is the kth degree B-spline basis functions. =i 0=j 0 where Ni,k (u) is the kth degree B-spline basis functions, N j,l (v) is the lth degree B-spline basis functions, d i, j is control vertices, m + 1 and n + 1 are the number of control vertices in u and v parametric directions respectively, u and v are two independent parameters which monotonically increase along the respective parametric spaces
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