In the present paper it is presented the flow around a 2D square cylinder which is located downstream of a splitter plate and at a certain distance of it. The fluid velocity below and above the splitter plate is different, several velocity ratios are considered, it is interesting to see that the downstream vortex shedding frequency and amplitude highly depends on the velocity ratio defined upstream. So far, the Reynolds numbers evaluated fall into the laminar unsteady regime, yet the interaction between the upstream mixing layer and the wake generate fully different downstream vortex shedding for different upstream velocity ratios, lift, drag and Strouhal numbers are as well highly dependent on the velocity ratios. In the present paper, the comparison between the results obtained via CFD finite volumes and Lattice Boltzmann Method are being presented. For these initial cases studied the agreement is very good.