In practical flow congurations, a large disparities of geometrical length scales are often encountered. Inside a combustor, for example, the ratio between the diameter of the injection holes and the size of the entire combustion chamber may present several orders of magnitude. When considering an explicit solver for fully compressible Navier-Stokes equations, the global time step is constrained through a CFL-like condition by the size of the smallest cells in the overall computational domain. Local renement of the injector leads to an inhomogeneous mesh and the former restriction drastically alters the overall solver effciency. A new local time-stepping (LTS) method is proposed to address this issue. The domain is divided into subgrids composed of cells that have similar sizes. Flow equations are simultaneously advanced on each subgrid which have a local time step adapted to satisfy the local CFL condition. The accuracy of the method has been veried on a simple convection case using a test code. The method has also been implemented in a large eddy simulation (LES) explicit solver and successfully tested for an acoustic wave propagation. It has been nally used in the two-dimensional large eddy simulation of a turbulent jet.