Asymptotic modeling of boundary layers in aeroacoustics

Taking into account the boundary shear layers of the mean flow in aeroacoustic compu- tations requires expensive mesh refinements, the size ε of the layer being small compared to the acoustic wavelength λ. On the other hand, neglecting these thin layers can reduce significantly the accuracy of the simulation, and even worse, it can lead in case of absorb- ing walls to an ill-posed problem, intractable numerically. The solution that we propose consists in deriving a new boundary condition which takes into account at the first order in ε / λ the presence of the boundary layer. Well-posedness and stability of the new problem are studied by a modal analysis. The results depend on the Mach profile of the boundary layer and, for an impedant wall, on the values of the impedance model. For instance, the problem with a linear or parabolic profile is stable for the case of a rigid boundary, and unstable but well-posed for an impedant boundary with a large impedance Z. Numerical validations are in progress.