Abstract
The present study aims to develop an efficient numerical method for computing the diffraction and radiation of water waves with horizontal long cylindrical structures, such as floating breakwaters in the coastal region, etc. A higher-order scheme is used to discretize geometry of the structure as well as the physical wave potentials. As the kernel of this method, Wehausen’s free-surface Green function is calculated by a newly-developed Gauss–Kronrod adaptive quadrature algorithm after elimination of its Cauchy-type singularities. To improve its computation efficiency, an analytical solution is derived for a fast evaluation of the Green function that needs to be implemented thousands of times. In addition, the OpenMP parallelization technique is applied to the formation of the influence coefficient matrix, significantly reducing the running CPU time. Computations are performed on wave-exciting forces and hydrodynamic coefficients for the long cylindrical structures, either floating or submerged. Comparison with other numerical and analytical methods demonstrates a good performance of the present method.
Highlights
Cylindrical structures have been widely used in the rapidly-developing coastal and offshore engineering industries in recent decades, in the form of such as floating breakwaters, oscillating water columns (OWC) for power generation, etc
Cylindrical structures are important in the industries probably due to their simplicity in geometry and the relatively lower fluid forces they may experience
The present work is very different from the classical research in the following aspects: (1) since the governing equation used is the Laplace equation instead of the Helmholtz equation, Wehausen’s free-surface Green function [10], constituted by several simple arithmetic functions, can be employed instead of Haskind’s Green function [5,11] which may require many evaluations of the modified Bessel functions; (2) since the free-surface Green function is used as the kernel instead of the Rankine Green function, meshing of the geometry could be restricted to only the body surface, such that there is no need to deal with the open boundaries, as has been
Summary
Cylindrical structures have been widely used in the rapidly-developing coastal and offshore engineering industries in recent decades, in the form of such as floating breakwaters, oscillating water columns (OWC) for power generation, etc. Green numerical function investigations for hydrodynamic performances of such thefunctions, above advantages facilitate en evaluated cylindrical in a faster speed with a precise result. Simplified two-dimensional model has many fewer unknowns on the body surface, since the surface he framework of linearThese potential flow theory, the structures present are so long in its axis direction that the problem to be solved horizontal cylindrical integrations have been in substituted by lineInintegrations. Green function are needed for each incident wave period, compared to applied to parallelize the algorithm on multi-processor machines Those (10 ) evaluations in discretization, the three-dimensional cases (see [12]).
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