This paper deals with a computational strategy suitable for the simulation of multiphysics problems and based on the Large Time INcrement (LATIN) method. One of the main issues in the design of advanced tools for the simulation of such problems is to take into account the different time and space scales which usually arise with the different physics. Here, we focus on using different time discretizations for each physic by introducing an interface with its own discretization. The proposed application concerns the simulation of a 2-physics problem: the fluid-structure interaction in porous media.