We introduce the star formation and Supernova (SN) feedback model of the SATIN (Simulating AGNs Through ISM with Non-Equilibrium Effects) project to simulate the evolution of the star forming multi-phase interstellar medium (ISM) of entire disk galaxies. This galaxy-wide implementation of a successful ISM feedback model naturally covers an order of magnitude in gas surface density, shear and radial motions. It is implemented in the adaptive mesh refinement code RAMSES at a peak resolution of 9 pc. New stars are represented by star cluster (sink) particles with individual SN delay times for massive stars. With SN feedback, cooling and gravity, the galactic ISM develops a realistic three-phase structure. The star formation rates naturally follow observed scaling relations for the local Milky Way gas surface density. SNe drive additional turbulence in the warm (300 K <
< 10 K) gas and
increase the kinetic energy of the cold gas, cooling out of the warm phase. The
majority of the gas leaving the galactic ISM is warm and hot with mass loading
factors of . While the hot gas is leaving the system, the
warm and cold gas falls back onto the disc in a galactic fountain flow.