Numerical analysis of the immersed boundary method applied to the flow around a forced oscillating cylinder

In present paper, Navier-Stokes and Continuity equations for incompressible ow around an oscillating cylinder were numerically solved. Sixth order compact dierence schemes were used to solve the spatial derivatives, while the time advance was carried out through second order Adams Bashforth accurate scheme. In order to represent the obstacle in the ow, the Immersed Boundary Method was adopted. In this method a force term is added to the Navier-Stokes equations representing the body. The simulations present results regarding the hydrodynamic coecients and vortex wakes in agreement to experimental and numerical previous works and the physical lock-in phenomenon was identied. Comparing dierent methods to impose the IBM, it can be concluded that no alterations regarding the vortex shedding mode were observed. The Immersed Boundary Method techniques used here can represent the surface of an oscillating cylinder in the ow.