An Application of Rankine Source Method for Unsteady Free Surface Flows

Abstract

Rankine Source Method is applied for unsteady free surface flows in this paper. In order to clarify the radiation condition of Rankine Source Method, eigen values and eigen vectors of the matrix obtained from a discrete boundary integral equation are investigated. And it is found that the radiation condition is satisfied by introducing a small variable ε which is equivalent to the artifice due to Rayleigh. For a examination of the new radiation condition, a wave field induced by a periodic source under the free surface is calculated. Calculated results are in good agreement with analytical ones. Wave forces acting on a virtical circlar cylinder with forward speed are also calculated. Results suggest that the present method is applicable to the calculation of the 3-dimensional unsteady free surface flow around a ship with forward speed.