There are many engineering applications in which separation and reattachment play dominant roles in the overall flow behavior (e.g., combustors, diffusers, flow around airfoils and buildings, etc.). Because of its geometrical simplicity, flow over a backward-facing step (BFS) is one of the most commonly studied turbulent boundary layer flows involving separation and reattachment. A principal motivation for the present study is the work of Le et al. (J. Fluid. Mech., vol.330, 1997) involving direct numerical simulations (DNS) of turbulent flow over a backward-facing step at a Reynolds number of 5000 (based on step height). In our ongoing investigation we consider the same geometry and flow parameters as those assumed by Le et al. but we restrict the study to two spatial dimensions. In particular, we consider both DNS and additive turbulent decomposition (ATD) simulations so as to allow for qualitative comparisons of both methods and the results reported by Le et al. An outline of the current method and some preliminary results will be presented and discussed at the talk.