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November  2014, 19(9): 2767-2783. doi: 10.3934/dcdsb.2014.19.2767

Straightforward approximation of the translating and pulsating free surface Green function

 1 Ship Science, University of Southampton, Southampton SO17 1BJ, United Kingdom

Received  October 2013 Revised  March 2014 Published  September 2014

The translating and pulsating free surface Green function represents the velocity potential of a three-dimensional free surface source advancing in waves. This function involves singular wave integral, which is troublesome in numerical computation. In the present study, a regular wave integral approach is developed for the discretisation of the singular wave integral in a whole space harmonic function expansion, which permits the free surface wave produced by the fluid motion to be decomposed by plane regular propagation waves. This approximation gives rise to a simple and straightforward evaluation of the Green function. The algorithm is validated from comparisons between present numerical results and existing numerical data.
Citation: Zhi-Min Chen. Straightforward approximation of the translating and pulsating free surface Green function. Discrete & Continuous Dynamical Systems - B, 2014, 19 (9) : 2767-2783. doi: 10.3934/dcdsb.2014.19.2767
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