Dissipative state formulations and numerical simulation of a porous medium for boundary absorbing control of aeroacoustic waves

Abstract : The problem under consideration relates to a model of porous wall devoted to aircraft motor noise reduction. For such a medium, the parameters of the propagation equation depend on the frequency, so the corresponding time-model involves non rational convolution operators. Consequently, the impedance of the wall is a non rational function of the frequency. On the basis of complex analysis and causality properties, we introduce infinite dimensional state formulations of these operators. The coupling of the so-obtained model with a standard aeroacoustic one then leads to a time-local system the analysis of which is simplified thanks to the existence of an energy functional in the sense of which the global dissipativity is insured. Some numerical results are given to illustrate the theoretical results.