Journal of Applied Mathematics
Volume 2012 (2012), Article ID 505916, 16 pages
Research Article

Numerical Prediction of Hydrodynamic Loading on Circular Cylinder Array in Oscillatory Flow Using Direct-Forcing Immersed Boundary Method

1Department of Mechanical Engineering, National Taiwan University of Science and Technology, Taipei 10607, Taiwan
2Ecological Engineering Research Center, National Taiwan University, Taipei 10617, Taiwan
3Department of Applied Mathematics, Feng Chia University, Taichung 40724, Taiwan

Received 20 January 2012; Revised 28 June 2012; Accepted 20 July 2012

Academic Editor: Carl M. Larsen

Copyright © 2012 Ming-Jyh Chern et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Cylindrical structures are commonly used in offshore engineering, for example, a tension-leg platform (TLP). Prediction of hydrodynamic loadings on those cylindrical structures is one of important issues in design of those marine structures. This study aims to provide a numerical model to simulate fluid-structure interaction around the cylindrical structures and to estimate those loadings using the direct-forcing immersed boundary method. Oscillatory flows are considered to simulate the flow caused by progressive waves in shallow water. Virtual forces due to the existence of those cylindrical structures are distributed in the fluid domain in the established immersed boundary model. As a results, influence of the marine structure on the fluid flow is included in the model. Furthermore, hydrodynamic loadings exerted on the marine structure are determined by the integral of virtual forces according to Newton’s third law. A square array of four cylinders is considered as the marine structure in this study. Time histories of inline and lift coefficients are provided in the numerical study. The proposed approach can be useful for scientists and engineers who would like to understand the interaction of the oscillatory flow with the cylinder array or to estimate hydrodynamic loading on the array of cylinders.