Numerical Study of 3D Pulsating Source Green Function of Finite Water Depth

Abstract

The accurate and efficient evaluation of the Green function and its derivatives for a pulsating source in finite water depth is one of the most important aspects in wave force calculation for offshore structures, at the same time it is also one of the most challenging tasks due to the singularity in the Cauchy principal value integral and the oscillation behavior of the Bessel function. In this paper, a new integral equation is proposed in which the singular term is deducted from the Green function. Furthermore, the Gauss-Laguerre integral equation proposed by other researcher has been improved to obtain a new form of the equation. Using these two proposed methods, numerical calculations are performed for the pulsating source Green function and its derivatives for finite water depth. The results show that very good agreements are achieved between the present results and other published data. The precision and efficiency of the present methods are also investigated and compared with the series solution and traditional Gauss-Laguerre integral method. It shows that both of the new methods have better precision than the traditional Gauss-Laguerre integral, but less efficient than the series solution. On the other side, the series solution would lose precision in the near-fields approaching zero, but the new Gauss-Laguerre integral equation could obtain right results. Furthermore the series solution has poor precision in large wave frequency and water depth in which case both of the new methods could obtain right results. Finally, one strategy has been proposed which could properly obtain the value of green function and its derivatives.