Numerical evaluation of three-dimensional water impact by the displacement potential formulation

The numerical accuracy of the displacement potential approach for a three-dimensional water-impact problem is investigated. An examination of the elliptic paraboloid shows that the boundary-value problem for the displacement potential, as well as the velocity potential, can be solved accurately, even if the panel size of the numerical scheme is no small enough. The numerical accuracy of the position of the contact line is poor. However, the accuracy of the virtual mass is good because of the averaging effect along the contact line. A comparison with Scolan and Korobkin's designed body confirms the accuracy of the drop speed and the penetration displacement. The displacement potential approach is extended to the case of water impact with trapped air. The numerical accuracy of the calculated air pressure in the cavity is confirmed by comparison with an experimental result. With these results, the suitability of the displacement potential approach to the ship-slamming problem is demonstrated.