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

Abstract

A fully nonlinear Numerical Towing Tank (NTT) is developed to simulate ship waves based on non-uniform rational B-spline (NURBS) surface and potential theory in the time domain. Fully nonlinear free surface boundary conditions and the exact body boundary condition are applied to solve the boundary value problem. The free surface and the ship hull surfaces are described precisely using NURBS formulation. Mixed Eulerian–Lagrangian (MEL) method is used to update the exact free surface based on material node approach. Isoparametric direct boundary integral equation (BIE) is used to compute the flow field. The intersection of the free surface and the rigid walls are found using an adaptive methodology based on NURBS and double nodes approach at each time step. To retain the open sea condition, a sponge layer is adopted on the exact free surface adjacent the tank's walls. To examine the accuracy of NURBS surface, the NURBS description of the ship hull for different orders of the basis function and different numbers of nodal points are compared with the exact surface. To verify the present computational algorithm, the solutions are compared with the experimental records and the prior numerical study for a Wigley hull. Propagation of the ship wave within the computational domain is studied due to ship advance in different water depths.