Calculation of Deep-Water Wash Waves Using a Combined Rankine/Kelvin Source Method

Abstract

This paper presents a method for computation of far-field wash waves in deep water. The method combines a nonlinear Rankine source method in an inner domain with a Kelvin source method for the far-field waves in an outer domain. Kelvin sources are distributed on a vertical matching wall, positioned at the outer edge of the inner domain. These sources are used to specify a boundary condition for the disturbance velocity potential on the matching wall. The boundary condition is used in the Rankine source solution of the inner domain. The size of the inner domain can be reduced in the transverse direction compared to a method using Rankine sources only, as the wave reflections at the edge of the inner domain are eliminated. Further, the far-field waves can be computed using the solution on the matching wall together with the Kelvin source distribution. The verification of the present method includes a comparison for a single Kelvin point source and a comparison to a Rankine source method at intermediate distances for the Wigley hull and for a catamaran. A grid dependence study for the position, size, and panel density on the matching wall is included for the Wigley hull. Computed and measured longitudinal wave cuts are compared for a catamaran both in the inner and the outer domain. Good agreement is obtained.