Ocean Systems Engineering

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A more efficient numerical evaluation of the green function in finite water depth

  • Xie, Zhitian (Department of Ocean Engineering, Texas A&M University) ;
  • Liu, Yujie (Department of Ocean Engineering, Texas A&M University) ;
  • Falzarano, Jeffrey (Department of Ocean Engineering, Texas A&M University)
  • Received : 2017.06.02
  • Accepted : 2017.09.19
  • Published : 2017.12.25
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Abstract

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.

Keywords

References

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