Computational Model of Unsteady Hydromechanics of Large Amplitude Gerstner Waves

¹ Saint Petersburg State University, Universitetskaya Emb. 7-9, 199034 St. Petersburg, Russia
² Alexey Krylov All-Russian Scientific Shipbuilder Society, Saint Petersburg, Russia

^★ e-mail: i.gankevich@spbu.ru

Published online: 20 January 2020

Abstract

The computational experiments in the ship fluid mechanics involve the nonstationary interaction of a ship hull with wave surfaces that include the formation of vortices, surfaces of jet discontinuities, and discontinuities in the fluid under the influence of negative pressure. These physical phenomena occur not only near the ship hull, but also at a distance where the waves break as a result of the interference of the sea waves with waves reflected from the hull. In the study reported here we simulate the wave breaking and reflection near the ship hull. The problem reduces to determining the wave kinematics on the moving boundary of a ship hull and the free boundary of the computational domain. We build a grid of large particles having the form of a parallelepiped and, in the wave equation instead of the velocity field we integrate streams of fluid represented by functions as smooth as the wave surface elevation field. We assume that within the boundaries of the computational domain the waves do not disperse, i.e. their length and period stay the same. Under this assumption, we simulate trochoidal Gerstner waves of a particular period. This approach allows to simulate the wave breaking and reflection near the ship hull. The goal of the research is to develop a new method of taking the wave reflection into account in the ship motion simulations as an alternative to the classic method which uses added masses.