Abstract Despite the development of Diesel particulate filters began in the eighties, it has not been till the recent years when the use of these systems has became widely spread as a technological solution to reduce particulate emissions. This is due to the continuously increasing restrictions of present and future emission control regulations which are close to the technological limit of other type of solutions based on the combustion process control. This renewed interest by Diesel particulate filters demands further experimental and theoretical research in order to optimize filter performance as well as engine matching. From the theoretical point of view, this double objective can be resolved with the use of a unique one-dimensional computational tool: wave action models. They are widely used in the study of air management in internal combustion engines. To adapt and extend their use for after-treatment systems analysis is needed the development of specific tools; chemical species transport through the engine or optimization of the calculation methodology in order to reduce the computational cost are the main aspects to be dealt with. Thus, the study converges towards a wave action model with the ability to calculate every aspect of the physical and chemical processes taking place in after-treatment devices. On the other hand, a key aspect is to grant the model with enough flexibility so that it can carry out analysis on any type of engine exhaust architecture, ensuring a correct interaction between the particulate filter and the rest of the engine components. It is therefore convenient to treat the flow in the particulate filter as unsteady, one-dimensional, compressible and non-homoentropic. These are the basic characteristics of the model presented in this work, which allows the radial discretization of the monolith in as many channel rings as required solving a pair of inlet-outlet channels in each of them. The model undergoes an experimental validation of progressive complexity: cold, steady flow offering optimal operation conditions for the development of methodologies aimed at the characterization of the porous media; cold, pulsating flow which allows to show the capacity of the model to reproduce the dynamics of the unsteady and compressible flow; and lastly, typical engine hot, pulsating flow which requires the development of an additional heat transfer sub-model specifically adapted to the characteristics of wall-flow monoliths. As a product of this work, a set of computational tools are obtained which allow the thermo-fluid-dynamic calculation of wall-flow Diesel particulate filters under any engine operation condition.