A semi-analytical pulsating source incorporated with the panel method for wave-body interactions

To deal with hydrodynamics, numerical integration of pulsating source Green's function over a panel is very important. However, little research is focused on it. In the present paper, a semi-analytical integral expression of pulsating source over the panel is proposed. A coordinate transformation is performed and the panel is mapped into a unit rectangle. The space integral is carried out beforehand. Thus, the integral of Green's function can be expressed as a theta-type single integral expression. Numerical results show that the present expression provides a new robust approach to obtain the integral of Green's function over a panel in an accurate and stable manner. Based on the above method, radiation-diffraction problems of Wigley III and LNG carrier in waves are calculated, then ship motion responses versus various wave frequencies are computed. The calculated motions of ship acquired agree well with experimental data.