The numerical simulations conducted in computational fluid dynamics (CFD) often ex- hibit strong multi-scale features. This can be due to the use of unstructured grids with highly heterogeneous refinement, and/or to a wide range of physical characteristic times. This is especially true in the field of energetics, where it is common to deal with compressible multiphase flows, with chemical reactions and turbulence. As a result, significant spatial variations in the CFL (Courant-Friedrichs-Lewy) number can be encountered. The stability of temporal integration methods, particularly explicit ones, mandates a maximum CFL number not to be exceeded, thereby imposing a maximum stability time step, theoretically different for each mesh cell. However in practice, the simulation time step must be uniform for unsteady calculations to preserve conservation and temporal consistency. This uniform time step is then dictated by the stability of the most restrictive cell. Hence, there is a clear interest in developing conservative and consistent local time-stepping methods to relax the constraint of a uniform time step for unsteady simulations. This can significantly optimize computation times, with a greater benefit for applications in which the distribution of CFL values is broad. In this work we present a zonal time-stepping method applicable to explicit Runge-Kutta methods, implemented within CEDRE, a multi-physics platform for industrial applications in energetics, using general unstructured meshes in the finite volume framework. The method follows the principles of some methods proposed in the literature. However, a specific effort has been made to allow the time step in each zone to evolve over time to match the CFL condition as closely as possible throughout the computation, keeping some flexibility in the timing of the different domains. Conservation is ensured through the application of corrective terms. After describing the method, it is illustrated on representative cases, and its benefits in term of computational efficiency are evaluated. Finally, some improvement perspectives are discussed.