A simple and efficient calculating method for multiple ships and piers in waves

A simple and efficient calculating method for multiple ships and piers in waves is presented.The method is approximating the ship section by a rectangle with the same area as that of the original ship section.Then,the flow field is divided into inner domain below the ship bottom and the outer domain beside ship hull.The velocity potential in inner domain is given by an analytic solution.The velocity potential in outer domain is expressed by a source-sink distribution along the contour of ship water area.The two potential solutions are matched at the interface of two domains.A vertical pier is equivalent to the ship with a zero gap between the ship bottom and the sea bed.This method is validated using measurement and other numerical results.The interactions of two and three ships mooring near a long rectangle pier are calculated and discussed.