The present work focuses on investigating the underlying flow physics behind the transition from periodicity to aperiodicity in the flow past a harmonically plunging elliptic foil as the plunge amplitude is increased to a high value. Two-dimensional (2D) numerical simulations have been performed in the low Reynolds number regime using an in-house flow solver developed following the discrete forcing Immersed Boundary Method (IBM). To capture the aperiodic transition in the unsteady flow-field behind a flapping foil accurately, the boundary structures such as the leading-edge vortex and its evolution with time need to be resolved with maximum accuracy as they are the primary key to the manifestation of the aperiodic onset. Even a small discrepancy may result in a different dynamical state and lead to an erroneous prediction of the transition route. On the other hand, discrete forcing IBM is known to suffer from non-physical spurious oscillations of the velocity and pressure field near the boundary, which may affect the overall flow-field solution. In this regard, the present work investigates the efficacy of discrete forcing IBM in accurately capturing the transitional dynamics in the flow-field around a plunging elliptic foil by comparing its results with that of a well-validated body-fitted ALE solver. © 2021, The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.