The efficiency of numerical simulation of wave propagation is highly dependent of the quality of the mesh. For complex simulations, the size of the cells in the mesh can strongly vary, either because of the geometry or because of the different propagation celerity of the waves.To ensure stability, explicit numerical schemes must match with the CFL conditions of every cells of the mesh. When significant disparities appear in the domain, the time step used on big cells is not optimal, which can cause heavy calculation cost and result in a loss of efficiency.To improve the performance of the programs, local time-stepping methods based on a spatial Discontinuous Galerkin discretization have been implemented. This document presents the comparison between three local time-stepping methods: a conservative method, a recursive method, and an asynchron method.The two first methods use local time steps that are fractions of the global time step, while the third method can use independent time steps on each cell of the mesh.The accuracy of the solution, the computation cost and the speedup of local-time stepping are presented on cases in two and three dimensions on configurations as fine slot or domains with geometric singularities.