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

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

1 DMPE, ONERA, Université de Toulouse [Toulouse]
2 DISC - Département d'Ingénierie des Systèmes Complexes

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

Mots clés: Fractional calculus; Diffusive representation; Discontinuous Galerkin; Time-delay systems; Time-domain impedance boundary condition

Domaines: Mathématique discrète [cs.DM]

Florian Monteghetti, Denis Matignon, Estelle Piot. Energy analysis and discretization of nonlinear impedance boundary conditions for the time-domain linearized Euler equations. Journal of Computational Physics, 2018, 375, pp.393-426. ⟨10.1016/j.jcp.2018.08.037⟩. ⟨hal-01920456⟩