Numerical Study of the Added Resistance of Ship Advancing in Waves Using Far-Field and Near-Field Methods

When a ship advances in a seaway, it undergoes 6-degree-of-freedom motion. The ship motions and wave loads are very important from operability and survivability points of view. The resistance increase due to waves is also important from the economic point of view. Although the accurate prediction of these seakeeping characteristics should be done using the unsteady CFD computations, the analytical method based on the linear potential flow theory have been widely used to evaluate them at the early design stage since the latter does not require large computing resources. In the present paper, the added resistance of a ship advancing in waves was calculated using both Maruo’s far-field formula and the near-field method. The radiation-diffraction potential over the wetted surface of the ship has been obtained using the three-dimensional frequency-domain forward-speed free-surface Green function (Brard 1948) and the forward-speed Green integral equation (Hong 2000). Numerical solutions are obtained by making use of the 9-node second-order inner collocation boundary element method (Hong et al. 2014b). In the present paper, Maruo’s far-field formula was combined with the exact three-dimensional Kochin function so that the added resistance thereby obtained could show good comparison with experimental results over the entire wave range including the short wave range. The near-field added resistance is the time mean value of the 2^nd-order forces acting on the advancing ship in waves. The time-mean hydrodynamic force, obtained by using direct integration of the hydrodynamic pressure due to the sum of the unsteady potential and steady potential approximated by the double-body potential over the wetted surface of the ship, was also presented. Comparison of the present far-field and simplified near-field numerical values and the experimental values reported by Journee (1992) of the added resistance for the Wigley ship models I and II has been made in order to find appropriate numerical values of the far-field added resistance over the entire frequency range of interest.