Approximate Models in Aeroacoustics
Date: Mon, Sep 21 2009
Location: Bizkaia Technology Park, Building 500 E-48160 DERIO - Basque Country- Spain
Speakers: Patrick Joly
In many applications in aeroacoustics, in particular in aeronautics, it is important to simulate the interactions of acoustic waves with boundaries (walls, wings,...). Moreover, boundary layers of very small width are present close to the boundaries.
The question of a satisfactory treatment of boundaries in aeroacoustics remains essentially open. In this work, we study acoustic wave propagation in a thin duct, in the presence of a laminated flow, a problem which can be seen as a first step towards the treatment of such boundary layers.
We use an asymptotic analysis when the width of the duct is small with respect to the wavelength, which amounts to a low frequency analysis, assuming that the Mach profile of the flow is obtained by a scaling of a reference profile M(y). We establish a limit model and study its well-posedness. On the one hand,we exhibit some profiles for which the model is strongly ill-posed and obtain, as a by-product, new instability results for compressible linearized Euler equations.
On the other hand, we establish sufficient conditions on M(y) for the model to be well-posed: the weak well-posedness of the Cauchy problem is obtained via a quasi-explicit representation of the solution, using the Fourier-Laplace transform in space-time. Numerical illustrations will be presented.
Finally, we shall show how these results can be used to construct effective boundary conditions for boundary layers.
Non-self-adjoint operators and their spectra
RGAS School on Singularities
Daniel Bath (KU Leuven), Eamon Quinlan-Gallego (U. Utah), Ilya Smirnov (BCAM Bilbao) and Guillem Blanco (KU Leuven)