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 associated time-model involves non rational convolution operators, which make the model complex from both analysis and 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 time-domain simulation of the porous wall and its impedance operator are given.