Use of Clement’s ODEs for the Speedup of Computation of the Green Function and its Derivatives for Floating or Submerged Bodies in Deep Water

A new acceleration technique for the computation of first order hydrodynamic coefficients for floating bodies in frequency domain and in deep water is proposed. It is based on the classical boundary element method (BEM) which requires solving a boundary integral equation for distributions of sources and/or dipoles and evaluating integrals of Kelvin’s Green function and its derivatives over panels. The Kelvin’s Green function includes two Rankine sources and a wave term. In present study, for the two Rankine sources, analytical integrations of strongly singular kernels are adopted for the linear density distributions. It is shown that these analytical integrations are more accurate and faster than numerical integrations. The wave term is obtained by solving Clément’s ordinary differential equations (ODEs) [1] and an adaptive numerical quadrature is performed for integrations over the panels. It is shown here that the computational time of the wave term by solving the ODEs is greatly reduced compared to the classical integration method [7].

The Water Depth Effect on Ship Pressure Distribution and Surface Wave

Applying linear marine hydrodynamics theory, the Kelvin wave source Green function of steady motion in finite depth was decomposed to three parts: array of simple Rankine sources, local distribution and wave part. Both at subcritical and supercritical speed, the singularity of integral function were eliminated by different integral path. The Kelvin source was distributed on the surface of ship by panel method, and the ship pressure distribution and wave pattern of ship in finite depth were calculated. The difference and connection between finite and infinite depth results were compared. It can provide the theoretical arithmetic base of improving the ship seaworthiness, increasing the speed and optimization of ship in river and offshore strip.