We present results from numerical simulations that study the interaction of a pair of twisted, buoyant magnetic flux tubes, which rise from the solar interior into the outer atmosphere of the Sun. The aim of our new model is to reproduce some of the dynamic solar phenomena in a self-consistent manner. We perform non-linear simulations in 2D and 3D numerical experiments by solving the compressible and resistive MHD equations using a Lagrangian remap, shock capturing code (Lare2D). For some aspects of the problem, we consider the evolution of the system using both uniform and locally enhanced resistivity. The two flux tubes start to rise at the same time but from a different height below the photosphere. The leading (first) tube, which is originally located nearer to the surface, rises and eventually expands above the photosphere forming a magnetized atmosphere for the upcoming system (second tube). Current sheets, high-velocity reconnection jets, plasmoids, loop brightnenings and arcade flare-like structures are formed, for the first time in such numerical experiments, self-consistently by the emergence, expansion and the dynamical interaction between the two emerging flux systems.