Among the strategies that could improve the efficiency of nowadays aircraft to decrease their carbon footprint, the reduction of aerodynamic drag is one of the most important. In that sense, friction drag is the main contributor to the total aerodynamic drag, and the delay or control of the processes that lead to the flow transition to turbulence plays a key role in the increase of aerodynamic efficiency. Receptivity is the mechanism that defines the way that disturbances penetrate into the boundary layer and have its origin in the incoming free-stream perturbations, in the surface roughness of the aerodynamic devices or in the interaction between them. This work will treat the numerical receptivity analysis of incompressible, two-dimensional boundary layers to free-stream turbulence, discrete roughness elements and their interaction; giving more knowledge about the physical mechanisms involved in the transition process and helping to the development of strategies to its delay and control, which can reduce the aerodynamic drag produced by turbulence. During several decades, the receptivity of two-dimensional boundary layers has been an intensive field of research. In this kind of flows, Tollmien-Schlichting waves are the main sources of instabilities and might be produced by perturbations like discrete roughness elements or free-stream turbulence, as it is described in \cite{saric}. In this work, the influence of the leading edge will be included in the analysis, using the well-known "modified super-ellipse", which is defined in the receptivity analysis to free-stream vorticity modes given by \cite{schrader}. The domain shape, size and base flow will be common with \cite{schrader} too. Additionally, isotropic free-stream turbulence will be generated at the far-field boundaries, following the work by \cite{schlatter} in a similar way to the one applied to a three-dimensional boundary layer case in \cite{vincentiis}. The receptivity to a discrete roughness element will be also an object of study, taking the experimental work from \cite{depaula} as a reference to establish its position along the flat plate chord (based on the roughness Reynolds number $Re_{kk}$) or its height (compared with the boundary layer displacement thickness at that location), as well as the boundary layer development along the flat plate geometry. Taking an experimental work as a reference will be useful to validate the numerical results obtained in this work.