Time-Domain volumic methods in electromagnetics, such as Finite-Difference (FDTD), Finite Integration Technique (FIT) or Transmission-Line Matrix (TLM) methods are investigated when dealing with structures that contain interfaces separating media with highly different constitutive parameters. Similar issues appear when dealing with adjacent irregular structured meshes with high step-size ratio. Simulation results show that these methods behave differently in a substantial manner. Some explanation is given to shed some light on the reason of this difference.