Numerical problems related to the convergence of the classical panel methods which are employed for the diffraction-radiation simulations are discussed. It is well known that, for the panel methods, the convergence issues are not exclusively related to the physical parameters (wave length, body shape, draught ...) but also to the one purely numerical phenomenon which occurs when the Boundary Integral Equation Method (BIEM) based on the use of Kelvin (wave) type Green’s function is used. Indeed, due to the fact that the Green’s function satisfies the free surface condition in the whole fluid domain below z = 0, the numerical solution is polluted, at some particular frequencies, by the solution of the unphysical problem inside the body. This phenomenon which is purely numerical, is known as the problem of irregular frequencies. From practical point of view, it is not always easy to distinguish if the irregularities in the final solution are coming, from the body mesh which is not fine enough, from the physical resonance of the system, from the problem of irregular frequencies or from something else!? In this paper the authors discuss these issues in the context of the evaluation of the seakeeping behavior of one typical FPSO (Floating Production Storage and Offloading). Both the linear (first order) as well as the second order quantities are of concern and the different methods for the elimination of the irregular frequencies are discussed. Special attention is given to the calculations of the different physical quantities at very high frequencies.
The numerical tool used within this research is the Bureau Veritas numerical code HYDROSTAR which is based on the panel method with singularities of constant strength.
Unified double- and single-sided homogeneous Green’s function representations
