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The present work focuses on the simulation of the hydrodynamics, transient filtration/loading and catalytic/NO2-assisted regeneration of Diesel after-treatment systems. A 1D unsteady model for compressible and reacting flows for the numerical simulation of the behavior of Diesel Oxidation Catalysts (DOCs) and Diesel Particulate Filters (DPFs) has been developed. The numerical model is able to keep track of the amount of soot in the flow; the increasing of back-pressure through the exhaust system (mainly due to the Diesel Particulate Filter) can be predicted by the calculation of the permeability variation of the porous wall, as the soot particles goes inside the DPF. A sub-model for the regeneration of the collected soot has been developed: the collected particulate is oxidized by the Oxygen (O2) and by the Nitrogen Dioxide (NO2).