When solving the forward speed hydrodynamic problem in frequency domain adopting the matching method with a meshless cylinder surface as the control surface, the simple Green function is used in the interior domain. To tackle the integration containing the first and second order derivatives of velocity potential on free surface about x, a method in which the velocity potential on the free surface and its derivatives are fitted by the cubic B spline is given, and the regular wave is chosen as the incident wave, and the theory solutions of its velocity potential and the first and second order derivatives about x are compared to the numerical solutions get from the cubic B spline.
The Computation of Higher Order Derivatives of Velocity Potential Based on B Spline Function
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Li, H, Lizhu, H, Ren, H, Chen, X, & Li, F. "The Computation of Higher Order Derivatives of Velocity Potential Based on B Spline Function." Proceedings of the ASME 2016 35th International Conference on Ocean, Offshore and Arctic Engineering. Volume 7: Ocean Engineering. Busan, South Korea. June 19–24, 2016. V007T06A011. ASME. https://doi.org/10.1115/OMAE2016-54407
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