Transient fully nonlinear ship waves using a three-dimensional NURBS numerical towing tank

Prediction of non-linear wave loads on large floating structures using a 3D numerical wave tank approach

“…Here the second-order forces and moments are obtained by summing several individual components, nearly all of which arise from the firstorder (linear) potential. According to one form [21], the 2nd order force ⃗ F (2) and moment ⃗ M (2) are given as…”

“…In Eqs. (12a, 12b), (1) and (2) are the total first-and second-order potential, ⃗ X is linear displacement at a point on S B (0) , ⃗ X G and ⃗ G are the translational and rotational acceleration of the body at C.G., R is the transformation matrix, and r is the relative vertical displacement at waterline wl . The terms r , ⃗ X , ⃗ X G , ⃗ G , and R in the above are all derived from the firstorder (linear) solution.…”

“…(12a, 12b) is the relative elevation term (I) followed by velocity-squared term (II), and then comes the acceleration potential term (III), the fourth term is the rotational component term (IV), and the fifth term is the second-order potential term (V). Except for the pressure arising from (2) , all other force components in the above result from the linearized total potential. As can be seen in Journee and Massie [21], the most dominant forces arise from the first two terms.…”

“…In the above, all the terms can be determined from the first-order perturbation potential (1) P except the fifth (last) term. This term, i.e., the contribution from the secondorder perturbation potential (2) P , requires solution of a separate 2nd order b.v.p. for this potential.…”

“…Some of the researches in this context have focused on the development and application of higher order spline-based boundary element methods (BEMs) with the aim of reducing the total number of meshes for the same level of accuracy achievable from a low-order BEM. These higher order BEMs are also being explored for their ability to better resolve some of the required interior parameters such as the spatial derivatives and body-free-surface intersection lines [1,2,5] compared to a low-order BEM. Alternative forms of BEM such as application of desingularized methods which enable a reduction in the total number of panels without sacrificing accuracy are also being explored [13].…”