Straightforward approximation of the translating and pulsating free surface Green function. (English) Zbl 1302.31010
Summary: 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.
MSC:
| 31B10 | Integral representations, integral operators, integral equations methods in higher dimensions |
| 35Q35 | PDEs in connection with fluid mechanics |
| 76B07 | Free-surface potential flows for incompressible inviscid fluids |
| 76B20 | Ship waves |
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