Suppression of Irregular Frequency Effect in Hydrodynamic Problems and Free-Surface Singularity Treatment

Abstract

Multibody operations are routinely performed in offshore activities, for example, the floating liquefied natural gas (FLNG) and liquefied natural gas carrier (LNGC) side-by-side offloading case. To understand the phenomenon occurring inside the gap is of growing interest to the offshore industry. One important issue is the existence of the irregular frequency effect. The effect can be confused with the physical resonance. Thus, it needs to be removed. An extensive survey of the previous approaches to the irregular frequency problem has been undertaken. The matrix formulated in the boundary integral equations will become nearly singular for some frequencies. The existence of numerical round-off errors will make the matrix still solvable by a direct solver, however, it will result in unreasonably large values in some aspects of the solution, namely, the irregular frequency effect. The removal of the irregular effect is important especially for multibody hydrodynamic analysis in identifying the physical resonances caused by the configuration of floaters. This paper will mainly discuss the lid method on the internal free surface. To reach a higher accuracy, the singularity resulting from the Green function needs special care. Each term in the wave Green function will be evaluated using the corresponding analysis methods. Specifically, an analytical integral method is proposed to treat the log singularity. Finally, results with and without irregular frequency removal will be shown to demonstrate the effectiveness of our proposed method.