Use of body-fixed coordinate system in analysis of weakly nonlinear wave–body problems

Second-order Taylor expansion boundary element method for the second-order wave radiation problem

“…It can be seen that the component due the second-order potential is dominant, so how to calculate the second-order potential accurately and effectively is important. Shao and Faltinsen [24] gives the history time solution of the same problem by the traditional high-order BEM under the earth coordinate system. The first-order derivatives are computed by the derivatives of the shape function, and the second-order gradients are calculated through the numerical differentiating of the shape function.…”

“…26 [24]. Teng [22] and Shao and Faltinsen [24] also pointed out that attention should be paid to in the computation of the first and second-order derivatives of the velocity potential. The components of the second-order loads acting on the forced surging and heaving vertical truncated cylinder are shown in Figs.…”

“…A truncated vertical cylinder under forced sinusoidal surge and heave motion has been solved to second-order by Isaacson and Ng [32] with time domain low-order direct BEM, Teng [22] with frequency domain high-order BEM, Shao and Faltinsen [24] with Fig. 1.…”

“…Teng [22] and Bai [23] use the Stokes theorem to eliminate the second-order derivatives and substitute by the first-order ones, which have to calculate the integration along its waterline and the Green function involving its first-order derivatives on body surface. Shao and Faltinsen [24] calculates the second-order wave loads under the body-fixed coordinated system without the derivatives of the velocity potential on the body boundary condition. However, the second-order derivatives still exist on the other surfaces.…”

Numerical analysis on springing and whipping using fully-coupled FSI models

“…Up to now, the 3-D potential theory with the weakly nonlinear approach is thought to be the most practical method for the fluid domain. In the future, nonlinear free surface body interactions should be solved for nonlinear springing analysis (Shao and Faltinsen, 2010). For consideration of slamming loads, 2-D methods are commonly used because 3-D method requires complicated treatment and heavy computational burden compared to the linear panel method of 3-D potential flow.…”