Modelling of water wave interaction with multiple cylinders of arbitrary shape

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Song, Hao
Tao, Longbin
Chakrabarti, Subrata
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2010
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Abstract

This paper describes the development of an efficient numerical model, namely scaled boundary finite-element method (SBFEM) for linear waves interaction with cylindrical structures of arbitrary shapes. The two-dimensional Helmholtz equation is firstly weakened in the circumferential direction, so that the governing partial differential equation is transformed to an ordinary matrix differential equation in radial direction, and is solved fully analytically. As a key element, a virtual porous circular cylinder surrounding the cylindrical structures is introduced so that the entire computational domain is partitioned along the virtual cylinder into an unbounded and several bounded sub-domains with common interfaces. The principle innovation is that, the present SBFEM model chooses Hankel function as a base solution for the unbounded sub-domain, while a power series is used for the internal bounded sub-domains. The approach discretises only the common interfaces of the sub-domains with surface finite-elements, and fewer elements are required to obtain very accurate results. Numerical simulations show that the new SBFEM model offers a considerable improvement by far in its numerical performance, as well as in the range of physical phenomena that is capable of simulating. The wave forces and run-ups are presented for a single and multiple cylindrical structures of different cross sectional shapes. Influences of the incident wave parameters and structural configurations on the hydrodynamics are examined.

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Journal of Computational Physics
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229
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5
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© 2010 Elsevier. This is the author-manuscript version of this paper. Reproduced in accordance with the copyright policy of the publisher. Please refer to the journal's website for access to the definitive, published version.
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Mathematical sciences
Theoretical and applied mechanics
Physical sciences
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