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

Florian Monteghetti (1) , Denis Matignon (2) , Estelle Piot (1) , Lucas Pascal (1)

1 ONERA - The French Aerospace Lab [Toulouse]
2 ISAE-SUPAERO - Institut Supérieur de l'Aéronautique et de l'Espace

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 (u0 = 0), where the complexity lies solely in the chosen impedance model. The existence of an asymptotically stable C0-semigroup of contractions is shown when the passive impedance admits a dissipative realisation; the only source of instability is the time-delay τ. The second part discusses the more challenging aeroacoustical case (u0 = 0), which is the subject of ongoing research. A discontinuous Galerkin discretisation is used to investigate both cases.

Mots clés: impedance boundary condition; diffusive representation; stability; discontinuous Galerkin

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [cs.NA]; Acoustique [physics.class-ph]

Florian Monteghetti, Denis Matignon, Estelle Piot, Lucas Pascal. Asymptotic stability of the linearised Euler equations with long-memory impedance boundary condition. 13th International Conference on Mathematical and Numerical Aspects of Wave Propagation (WAVES 2017), May 2017, Minneapolis, United States. ⟨hal-01618060⟩