A Mathematical Modeling Method for an Analytical Solution of Ship Hydrodynamic Pressure Fields in Complex Restricted Waters

Abstract

A ship advancing in restricted waters may cause a change in the surrounding velocity field, which in turn results in the hydrodynamic pressure field according to the variations in the ship speed. Accurate prediction of ship hydrodynamic pressure fields in restricted waters is therefore essential and important in the military and engineering fields. Based on the potential flow theory and the thin-ship assumption, dividing complex restricted waters with varying depths into the inner and outer domains with constant depths, a mathematical modeling method is developed and carried out for analyzing and solving the partial differential equations consisting of the governing equation with a dispersion effect, initial and boundary conditions, then the analytical solution of hydrodynamic pressure field caused by a ship advancing in complex restricted waters is obtained. The continuity of the analytical solution is confirmed and the correctness of the analytical solution is validated by simplifying to a simple water and comparing with available data. Moreover, the mathematical modeling method can be extended to study the hydrodynamic problems of ships in more complex waters.