Residual‐based stabilization of the finite element approximation to the acoustic perturbation equations for low Mach number aeroacoustics |
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| Authors: | Oriol Guasch Patricia Sánchez‐Martín Arnau Pont Joan Baiges Ramon Codina |
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| Affiliation: | 1. GTM ‐ Grup de recerca en Tecnologies Mèdia, La Salle, Universitat Ramon Llull, C/ Quatre Camins 2, 08022 Barcelona, Catalonia;2. Universitat Politècnica de Catalunya, C/ Jordi Girona 1‐3, Edifici C1, 08034 Barcelona, Catalonia |
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| Abstract: | The acoustic perturbation equations (APE) are suitable to predict aerodynamic noise in the presence of a non‐uniform mean flow. As for any hybrid computational aeroacoustics approach, a first computational fluid dynamics simulation is carried out from which the mean flow characteristics and acoustic sources are obtained. In a second step, the APE are solved to get the acoustic pressure and particle velocity fields. However, resorting to the finite element method (FEM) for that purpose is not straightforward. Whereas mixed finite elements satisfying an appropriate inf–sup compatibility condition can be built in the case of no mean flow, that is, for the standard wave equation in mixed form, these are difficult to implement and their good performance is yet to be checked for more complex wave operators. As a consequence, strong simplifying assumptions are usually considered when solving the APE with FEM. It is possible to avoid them by resorting to stabilized formulations. In this work, a residual‐based stabilized FEM is presented for the APE at low Mach numbers, which allows one to deal with the APE convective and reaction terms in its full extent. The key of the approach resides in the design of the matrix of stabilization parameters. The performance of the formulation and the contributions of the different terms in the equations are tested for an acoustic pulse propagating in sheared‐solenoidal mean flow, and for the aeolian tone generated by flow past a two‐dimensional cylinder. Copyright © 2016 John Wiley & Sons, Ltd. |
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| Keywords: | acoustics aeroacoustics stabilized FEM variational multiscale (VMS) finite element subsonic |
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