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Energy analysis and discretization of nonlinear impedance boundary conditions for the time-domain linearized Euler equations

Monteghetti, Florian and Matignon, Denis and Piot, Estelle Energy analysis and discretization of nonlinear impedance boundary conditions for the time-domain linearized Euler equations. (2018) Journal of Computational Physics, 375. 393-426. ISSN 0021-9991

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Official URL: https://doi.org/10.1016/j.jcp.2018.08.037

Abstract

Time-domain impedance boundary conditions (TDIBCs) can be enforced using the impeda-nce, the admittance, or the scattering operator. This article demonstrates the computational advantage of the last, even for nonlinear TDIBCs, with the linearized Euler equations. This is achieved by a systematic semi-discrete energy analysis of the weak enforcement of a generic nonlinear TDIBC in a discontinuous Galerkin finite element method. In particular, the analysis highlights that the sole definition of a discrete model is not enough to fully define a TDIBC. To support the analysis, an elementary physical nonlinear scattering operator is derived and its computational properties are investigated in an impedance tube. Then, the derivation of time-delayed broadband TDIBCs from physical reflection coefficient models is carried out for single degree of freedom acoustical liners. A high-order discretization of the derived time-local formulation, which consists in composing a set of ordinary differential equations with a transport equation, is applied to two flow ducts

Item Type:Article
HAL Id:hal-01920456
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
French research institutions > Office National d'Etudes et Recherches Aérospatiales - ONERA (FRANCE)
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Deposited By: Denis Matignon
Deposited On:13 Nov 2018 10:27

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