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Modelling and Simulation in Engineering
Volume 2014 (2014), Article ID 708372, 13 pages
Research Article

Computation of Pressure Fields around a Two-Dimensional Circular Cylinder Using the Vortex-In-Cell and Penalization Methods

1Research Institute of Marine Systems Engineering, Seoul National University, Seoul 151-744, Republic of Korea
2Department of Naval Architecture and Ocean Engineering, Seoul National University, Seoul 151-744, Republic of Korea

Received 8 January 2014; Revised 20 March 2014; Accepted 25 March 2014; Published 25 May 2014

Academic Editor: Franco Ramírez

Copyright © 2014 Seung-Jae Lee 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.


The vorticity-velocity formulation of the Navier-Stokes equations allows purely kinematical problems to be decoupled from the pressure term, since the pressure is eliminated by applying the curl operator. The Vortex-In-Cell (VIC) method, which is based on the vorticity-velocity formulation, offers particle-mesh algorithms to numerically simulate flows past a solid body. The penalization method is used to enforce boundary conditions at a body surface with a decoupling between body boundaries and computational grids. Its main advantage is a highly efficient implementation for solid boundaries of arbitrary complexity on Cartesian grids. We present an efficient algorithm to numerically implement the vorticity-velocity-pressure formulation including a penalty term to simulate the pressure fields around a solid body. In vorticity-based methods, pressure field can be independently computed from the solution procedure for vorticity. This clearly simplifies the implementation and reduces the computational cost. Obtaining the pressure field at any fixed time represents the most challenging goal of this study. We validate the implementation by numerical simulations of an incompressible viscous flow around an impulsively started circular cylinder in a wide range of Reynolds numbers: Re , 550, 3000, and 9500.