The Mediterranean region is frequently affected by heavy precipitation that produce flash-floods and landslides. They are the most damaging natural risk in Mediterranean that costs each year several billions euros of damages and fatalities. Mesoscale convective systems that stay over the same area during several hours are the main responsible for high rainfall totals that produce flash-flooding. These meteorological phenomena result from complex multiscale interactions between the ambient flow, topography and deep atmospheric convection that make difficult the forecast of the precise timing and location of the intense convective precipitation. The overarching objective of the MUSIC project is to provide a better understanding and modelling of intense convective precipitation events in Mediterranean in order to improve their forecast by state-of-art kilometric and sub-kilometric scale Numerical Weather Prediction (NWP) models. To reach this objective: (1) The project strongly relies on the observations collected during the HyMeX SOP1 field campaign that took place in northwestern Mediterranean (France, Italy, Spain) from 5 Sep. to 6 Nov. 2012. This major field campaign provides a novel and unique dataset of observations of the convective systems as well as of the ambient flow over the northwestern Mediterranean. (2) The project concentrates on the key physical parameterizations that strongly influence the forecasts of deep convection at kilometric and sub-kilometric scales: (i) the modelling of microphysical processes that is a leading order contributor to NWP precipitation forecast errors and (ii) the modelling of the turbulence in boundary layer and in and near convective clouds that influences the convection initiation and cloud growth. (3) The project makes use of the novel capabilities of large-grid simulations on massively-parallel scalar supercomputers to explicitly resolve (i) at sub-kilometric scale the multiscale interactions between convective and larger scale processes leading to heavy precipitation events in order to progress in their understanding and (ii) turbulence and microphysics within convective systems and in boundary layer through Large Eddy Simulations. The process studies led in MUSIC as well as these high-resolution large-grid simulations will supply references and guidelines for, in the future, improving and validating deep convection/microphysical/turbulence parameterizations of regional climate models, which are essential in the simulation of precipitation extremes.