We propose a new numerical code based on a new multi-species theoretical model to study the mass, momentum and energy exchanges (MMEE) that happen across the magnetospheric boundaries. We use two distinct populations for ions, one cold and one hot (plus one neutralising electron population), to take into account the differences between the properties of the plasmas coming from the magnetosphere and from the solar wind. This approach represents a step forward in the context of the study of coupled large-scale plasma systems being a new and efficient compromise between fluid and kinetic codes in tracing the different plasma contributions during MMEE. Due to the very important role that magnetic reconnection plays in connecting the shocked Solar Wind to the Earth's magnetosphere, we show and discuss the results we obtained about the simulations of the tearing mode instability occurring across an Earth's magnetopause that we modelled thanks to our most recents MMS observations [Rezeau 2018]. &