Super-Time Stepping methods are a family of numerical integration methods based on the use of a multi-step explicit scheme, in order to lower the stability constraints on the Fourier and CFL numbers to integrate parabolic partial differential equations. These methods therefore enable a computation time reduction compared to more limited classical explicit methods, while guaranteeing a second-order approximation. In this study, the general formulation of Super-Time Stepping schemes is first presented and applied to the simulation of diffusion-advection problems in anisotropic reactive porous materials encountered in the field of fire safety. An acceleration factor up to 5 is obtained against state-of-the-art second-order Runge-Kutta schemes. In the second part of the study, focus is made on the development of a Local Super-Time Stepping method improving the original integration schemes. The main idea is to locally reduce the time step by adjusting the number of steps of the integration scheme depending on local features of the physical problem to be solved, minimising the number of evaluations of the right-hand-side of the system of equations. This improvement is of particular interest for diffusion-advection problems in anisotropic reactive porous materials, where high pressure gradients and gas velocities are generally concentrated in areas exposed to heat sources. The zonal time step adjustment greatly improves the computation time in this configuration, where the time step is increased in most of the computation domain while keeping a second-order scheme. The third part of this study aims at evaluating the possible acceleration expected for both steady and unsteady simulations, in diffusive-only and diffusive-advective-reactive setups.