Waves' numerical dispersion and damping due to discrete dispersion relation

Abstract

In linear Rankine panel method, the discrete linear dispersion relation is solved on a discrete free-surface to capture the free-surface waves generated due to wave-body interactions. Discretization introduces numerical damping and dispersion, which depend on the discretization order and the chosen methods for differentiation in time and space. The numerical properties of a linear Rankine panel method, based on a direct boundary integral formulation, for capturing two and three dimensional free-surface waves were studied. Different discretization orders and differentiation methods were considered, focusing on the linear distribution and finite difference schemes. The possible sources for numerical instabilities were addressed. A series of cases with and without forward speed was selected, and numerical investigations are presented. For the waves in three dimensions, the influence of the panels’ aspect ratio and the waves’ angle were considered. It has been shown that using the cancellation effects of different differentiation schemes the accuracy of the numerical method could be improved.