Numerical Analysis of Rankine Source Collocation Method for the Steady Wave Making Resistance Problem

Abstract

The so called previous collocation technic, which was applied to satisfy the wave radiation condition in the Rankine source method, has often induced some unstable conditions to solve the steady wave making problems for commercial ships. These troubles prevented us from practical uses of the above collocation method to apply to the practical hull form design.The present author, trying to overcome these troubles, discusses the following instability problems caused by Rankine source collocation method.(a) Steep inclination of oblique grid causes unstable conditions to solve the free surface problems.(b) Very low speed condition generates singular state.(c) Very high speed condition also makes unnatural wave deformation in near flow field around a ship.In order to avoid above problems, some practical ideas including technics are considered as following manners;(a) In case of steeply inclined grid and low speed condition, improvement of free surface matrix of Rankine source is needed to avoid the unstable condition.(b) In high speed condition the inverse image flow system is helpful as a basic flow of Rankine source method.To validate that these ideas are efficient, the author programmed several Rankine source programs and applied them to some practical problems. Through these analyses, the author shows that the present improved collocation technic, if carefully applied, leads to a good result and becomes a useful tool for preliminary hull form design. In addition, the author proves that the Conjugate Gradient method, that is a kind of iterative and memory saving algorithm, is recommendable to solve a fragile linear simultaneous equation generated by Rankine source method.