Asymptotic stability of the linearised Euler equations with long-memory impedance boundary condition

Monteghetti, Florian and Matignon, Denis and Piot, Estelle and Pascal, Lucas Asymptotic stability of the linearised Euler equations with long-memory impedance boundary condition. (2017) In: 13th International Conference on Mathematical and Numerical Aspects of Wave Propagation (WAVES 2017), 15 May 2017 - 19 May 2017 (Minneapolis, United States).

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Abstract

This work focuses on the well-posedness and stability of the linearised Euler equations (1) with impedance boundary condition (2,3). The first part covers the acoustical case ($u_0 = 0$), where the complexity lies solely in the chosen impedance model. The existence of an asymptotically stable $C_0$-semigroup of contractions is shown when the passive impedance admits a dissipative realisation; the only source of instability is the time-delay $\tau$. The second part discusses the more challenging aeroacoustical case($u_0 \neq 0$), which is the subject of ongoing research. A discontinuous Galerkin discretisation is used to investigate both cases.

Item Type: Conference or Workshop Item (Paper) International conference proceedings 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) ONERA and DGA download 13 Jun 2018 11:09

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