In this article a two dimensional incompressible viscous flow past a square cylinder oscillating in cross flow with zero and 45 degree angles of attack is numerically studied by a Characteristics Based Splitter (CBS) finite element method. The solver is coupled to a mesh movement scheme using the Arbitrary Lagrangian-Eulerian (ALE) formulation to account for the body motion in the flow field. First, the accuracy of the numerical code is tested by comparing the numerical results obtained for the flow over the stationary square cylinder at the three different Reynolds numbers (Re = 100, 200, and 300) with the experimental data available. Then, the numerical results for the square cylinder undergoing transverse oscillations in the two angles of attack at different values of frequency and amplitude are investigated to determine the lock-on region. The results indicate physical similarity between circular and square cylinders concerning lock-on regions. Also the effect of lock-on phenomenon on the flow field pattern and time-averaged drag coefficient is investigated.
