[eng] A new limited-area numerical model (TRAM, for Triangle-based Regional Atmospheric Model) has been built using a nonhydrostatic and fully compressible version of the Navier-Stokes equations. Advection terms are solved using a Reconstruct-Evolve-Average (REA) strategy over the computational cells. These cells consist of equilateral triangles in the horizontal. The classical z-coordinate is used in the vertical, allowing arbitrary stretching (e.g. higher resolution in the Planetary Boundary Layer, PBL). Proper treatment of terrain slopes in the bottom boundary conditions allows for representing accurately the orographic forcing. To gain computational efficiency, time-splitting is used to integrate separately fast and slow terms and acoustic modes in the vertical are solved implicitly. For real cases on the globe, the Lambert map projection is applied, and all Coriolis and curvature terms are retained. No explicit filters are needed. The first part of the manuscript describes the dynamical core of the model and provides its thorough validation using a variety of benchmark tests (mostly in two dimensions) in the context of a dry-adiabatic atmosphere. In the second part, TRAM is reformulated for a moist atmosphere and is completed with a proper set of physical parameterizations of cloud microphysics, cumulus convection, short and long-wave radiation, PBL processes and surface fluxes. Various examples of the great versatility offered by this full version will be presented, with special emphasis on Mediterranean case studies. In summary, TRAM performs as well as state-of-the-art numerical models and is suitable to simulate circulations ranging from small-scale thermal bubbles (≈ 100 m scale) to synoptic-scale baroclinic cyclones (> 1000 km size), including orographic circulations, thermally driven flows, squall lines, supercells, all kinds of precipitation systems and medicanes. Besides opening a myriad of academic and research applications, TRAM regional forecasts at different resolutions are being disseminated in the web (see https://meteo.uib.es/tram).