Fully nonlinear and linear ship waves modelling using the potential numerical towing tank and NURBS

Waves induced by the ship advance in the calm water are simulated in a potential Numerical Towing Tank based on both the fully nonlinear approach and the linear theory. In the linear theory, a modified Green function, which was derived based on linearized free surface boundary conditions and the image method is used as a fundamental solution in the boundary integral equation. High-order boundary integral equation is used to solve the boundary value problem with Non-Uniform Rational B-Spline (NURBS) basis function. On the other hand, the time domain simulation of the fully nonlinear free surface flow due to the steady flow past over a ship model is conducted based on the Mixed Eulerian-Lagrangian approach. NURBS surface is used to describe the ship hull and the fully nonlinear free surface evolution. The numerical solutions are compared with a prior experimental study to verify both numerical models. In addition, the effect of nonlinear terms in fully nonlinear free surface boundary conditions is investigated. The wave making resistance as an essential criterion is compared with the experimental data and some numerical efforts to investigate the accuracy of both models. The capability of the modified Green function is also examined to simulate the ship waves in rectangular channels.