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Construction and analysis of an adapted spectral finite element method to convective acoustic equations

Andreas Hüppe 1 Gary Cohen 2 Sebastien Imperiale 3 Manfred Kaltenbacher 1
2 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
3 M3DISIM - Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine
LMS - Laboratoire de mécanique des solides, Inria Saclay - Ile de France
Abstract : The paper addresses the construction of a non spurious mixed spectral finite element (FE) method to problems in the field of computational aeroacous-tics. Based on a computational scheme for the conservation equations of linear acoustics, the extension towards convected wave propagation is investigated. In aeroacoustic applications, the mean flow effects can have a significant impact on the generated sound field even for smaller Mach numbers. For those convec-tive terms, the initial spectral FE discretization leads to non-physical, spurious solutions. Therefore, a regularization procedure is proposed and qualitatively investigated by means of discrete eigenvalues analysis of the discrete operator in space. A study of convergence and an application of the proposed scheme to simulate the flow induced sound generation in the process of human phonation underlines stability and validity.
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Andreas Hüppe, Gary Cohen, Sebastien Imperiale, Manfred Kaltenbacher. Construction and analysis of an adapted spectral finite element method to convective acoustic equations. Communications in Computational Physics, Global Science Press, 2016, ⟨10.4208/cicp.250515.161115a⟩. ⟨hal-01363149⟩

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