François Madiot: July 11, 2012

We focus now our attention on the acoustic scattering in a subsonic flow. Our objective is to develop a numerical method to solve linearized problem in time -harmonic regime in an unbounded domain and in a quite general case, in the sense that the geometry and therefore the mean flow can be complex. Contrary to the classical case when the fluid is at rest, the presence of the mean flow generally couples two different phenomena: acoustic propagation and convection of vortices. Up to our knowledge, only the potential case, which leads to a Helmholtz like scalar equation, has been completely handled. But this potential equation is only available in specific case in particular when the flow is irrotational and so when the coupling between acoustic and hydrodynamic effects are neglected. We want to extend this approach in more general cases. We have proposed to write an augmented equation by introducing a new variable $\xi$. This latter is directly linked to the vorticity of the flow and for example is equal to zero when the flow is irrotational. This variable is obtained through a time harmonic advection equation. So we obtain a coupled system where there are a scalar unknown the potential $\phi$ and a vector unknown $\xi$. So we use the Lagrange Finite Elements for the displacement $\phi$ and a Discontinuous Galerkin scheme for the new unknown $\xi$. This approach is implemented in 3D and first results are obtained.