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Ocean Systems Engineering   Volume 7, Number 4, December 2017, pages 399-412
DOI: https://doi.org/10.12989/ose.2017.7.4.399
 
A more efficient numerical evaluation of the green function in finite water depth
Zhitian Xie, Yujie Liu and Jeffrey Falzarano

 
Abstract     [Buy Article]
    The Gauss-Legendre integral method is applied to numerically evaluate the Green function and its derivatives in finite water depth. In this method, the singular point of the function in the traditional integral equation can be avoided. Moreover, based on the improved Gauss-Laguerre integral method proposed in the previous research, a new methodology is developed through the Gauss-Legendre integral. Using this new methodology, the Green function with the field and source points near the water surface can be obtained, which is less mentioned in the previous research. The accuracy and efficiency of this new method is investigated. The numerical results using a Gauss-Legendre integral method show good agreements with other numerical results of direct calculations and series form in the far field. Furthermore, the cases with the field and source points near the water surface are also considered. Considering the computational efficiency, the method using the Gauss-Legendre integral proposed in this paper could obtain the accurate numerical results of the Green function and its derivatives in finite water depth and can be adopted in the near field.
 
Key Words
    green function; finite water depth; numerical evaluation; Gauss-Legendre integral
 
Address
Zhitian Xie, Yujie Liu and Jeffrey Falzarano: Department of Ocean Engineering, Texas A&M University, College Station, Texas, USA 77840
 

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