Volume 11, Issue 2
Time-Harmonic Acoustic Scattering in a Complex Flow: A Full Coupling Between Acoustics and Hydrodynamics

A. S. Bonnet-Ben Dhia, J. F. Mercier, F. Millot, S. Pernet & E. Peynaud

Commun. Comput. Phys., 11 (2012), pp. 555-572.

Published online: 2012-12

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  • Abstract

For the numerical simulation of time harmonic acoustic scattering in a complex geometry, in presence of an arbitrary mean flow, the main difficulty is the coexistence and the coupling of two very different phenomena: acoustic propagation and convection of vortices. We consider a linearized formulation coupling an augmented Galbrun equation (for the perturbation of displacement) with a time harmonic convection equation (for the vortices). We first establish the well-posedness of this time harmonic convection equation in the appropriate mathematical framework. Then the complete problem, with Perfectly Matched Layers at the artificial boundaries, is proved to be coercive + compact, and a hybrid numerical method for the solution is proposed, coupling finite elements for the Galbrun equation and a Discontinuous Galerkin scheme for the convection equation. Finally a 2D numerical result shows the efficiency of the method.

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@Article{CiCP-11-555, author = {}, title = {Time-Harmonic Acoustic Scattering in a Complex Flow: A Full Coupling Between Acoustics and Hydrodynamics}, journal = {Communications in Computational Physics}, year = {2012}, volume = {11}, number = {2}, pages = {555--572}, abstract = {

For the numerical simulation of time harmonic acoustic scattering in a complex geometry, in presence of an arbitrary mean flow, the main difficulty is the coexistence and the coupling of two very different phenomena: acoustic propagation and convection of vortices. We consider a linearized formulation coupling an augmented Galbrun equation (for the perturbation of displacement) with a time harmonic convection equation (for the vortices). We first establish the well-posedness of this time harmonic convection equation in the appropriate mathematical framework. Then the complete problem, with Perfectly Matched Layers at the artificial boundaries, is proved to be coercive + compact, and a hybrid numerical method for the solution is proposed, coupling finite elements for the Galbrun equation and a Discontinuous Galerkin scheme for the convection equation. Finally a 2D numerical result shows the efficiency of the method.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.221209.030111s}, url = {http://global-sci.org/intro/article_detail/cicp/7378.html} }
TY - JOUR T1 - Time-Harmonic Acoustic Scattering in a Complex Flow: A Full Coupling Between Acoustics and Hydrodynamics JO - Communications in Computational Physics VL - 2 SP - 555 EP - 572 PY - 2012 DA - 2012/12 SN - 11 DO - http://doi.org/10.4208/cicp.221209.030111s UR - https://global-sci.org/intro/article_detail/cicp/7378.html KW - AB -

For the numerical simulation of time harmonic acoustic scattering in a complex geometry, in presence of an arbitrary mean flow, the main difficulty is the coexistence and the coupling of two very different phenomena: acoustic propagation and convection of vortices. We consider a linearized formulation coupling an augmented Galbrun equation (for the perturbation of displacement) with a time harmonic convection equation (for the vortices). We first establish the well-posedness of this time harmonic convection equation in the appropriate mathematical framework. Then the complete problem, with Perfectly Matched Layers at the artificial boundaries, is proved to be coercive + compact, and a hybrid numerical method for the solution is proposed, coupling finite elements for the Galbrun equation and a Discontinuous Galerkin scheme for the convection equation. Finally a 2D numerical result shows the efficiency of the method.

A. S. Bonnet-Ben Dhia, J. F. Mercier, F. Millot, S. Pernet & E. Peynaud. (2020). Time-Harmonic Acoustic Scattering in a Complex Flow: A Full Coupling Between Acoustics and Hydrodynamics. Communications in Computational Physics. 11 (2). 555-572. doi:10.4208/cicp.221209.030111s
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