The physics of supersonic combustion is analyzed in order to derive a new subgrid scale model for Large Eddy Simulation. Anisotropy associated to the directional Mach number typical of supersonic flows (i. e., M > 1 in only one direction) is explicitly considered by means of non-dimensionalized Navier-Stokes equations. The study shows that high Mach number flows experience mainly streamwise vorticity and consequently maximum helicity. Both affect mixing and may alter the turbulent kinetic energy decay by decreasing its rate, i.e., decreasing its characteristic spectral slope below that predicted by Kolmogorov scaling. Furthermore, it is analytically predicted that transversal pressure gradients increase vorticity, thus plausibly explaining the improved mixing realized by certain injectors. The supersonic regime is also found to affect the combustion regime: analysis of characteristic acoustic and convective times shows that while subsonic combustion takes place at approximately constant pressure, supersonic combustion takes place at approximately constant volume. Furthermore, collisional frequency is shown to increase due to local dilatation, resulting in faster kinetics and shorter ignition delay times. This effect could explain flame anchoring observed in some SCRJ combustor experiments. All the physical features and aspects of supersonic combustion found are used as ingredients to build a new subgrid scale model. In particular, micro-scale physics has been included by means of a subgrid kinetic energy equation that is algebraically modeled to provide the velocity fluctuation needed by the eddy viscosity SGS closure. Numerical simulations of a supersonic combustion NASA – Langley test case provide qualitative validation of the proposed model.