Effects of the terms associated with phi(zz) in free surface condition on the attitudes and resistance of different ships

One of approaches for numerical simulation of a ship moving in a still water is based on the composition of double-body flow and wavy flow solved by a boundary element method. There are several terms related to the second order derivative (ϕzz) of double-body flow velocity potential with respect to the vertical coordinate in the free surface conditions. Understanding of the effects of the terms is very limited so far. In many cases, they are just ignored even for ships with a high forward speed, particularly in the cases associated with multihull ships, for which no investigations on their effects have been found. This paper will present a study on the effects of the terms on the numerical prediction of the attitudes and resistance of different ships in various situations, including monohull, catamaran and trimaran with different parameters and at different Froude numbers. The results will demonstrate that the effects of the terms are significant in many cases and that considering this term may lead to the results similar to those obtained by fully nonlinear models at high Froude numbers