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)

1 TU Wien - Vienna University of Technology = Technische Universität Wien
2 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
3 M3DISIM - Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine

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.

Mots clés: Spectral Finite Elements; Aeroacoustics; Perturbation Equations

Domaines: Equations aux dérivées partielles [math.AP]

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, 2016, ⟨10.4208/cicp.250515.161115a⟩. ⟨hal-01363149⟩