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Analysis, simulation and impedance operator of a nonlocal model of porous medium for acoustic control

The problem under consideration relates to a model of a porous wall devoted to aircraft motor noise reduction. For such a medium, the parameters of the propagation equation depend on the frequency. Then, the corresponding time model involves nonrational convolution operators, which make the model complex from both the analysis and the simulation points of view. In this paper, based on the so-called diffusive representation of convolution operators, a time-local formulation of the porous wall model, well adapted to analysis and numerical simulation, is established and analyzed. Then its associated impedance operator is computed. Finally some numerical results relating to the simulation of the porous wall and to the one of its impedance operator are given to highlight the theoretical part.