On the Numerical Radiation Condition in the Steady-State Ship Wave Problem

Abstract

The waves created by a thin ship sailing in calm water are examined. The velocity potential of the ship in the zero Froude number case is known and the additional potential due to the waves is calculated by the Green function technique. The simple Green function corresponding to the Rankine source potential is used here. Two major problems exist with this method. In the Neumann-Poisson boundary-value problem- probably the first iteration toward a full nonlinear solution to the ship wave problem _it is necessary to impose a radiation condition in order to get uniqueness. This problem is related to the second one, which arises due to the existence of eigensolutions. The two-dimensional situation is here analyzed first, thereby easing the three-dimensional analysis. A numerical scheme is constructed and results for the twodimensional waves generated by a submerged vortex and for the three-dimensional waves due to the Wigley hull are presented.