Juliette Chabassier

selected publications

1. JSV

   Transmission line coefficients for viscothermal acoustics in conical tubes

   Thibault, Alexis,  Chabassier, Juliette, Boutin, Henri, and Hélie, Thomas

   Journal of Sound and Vibration Oct 2022

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   Viscothermal acoustic propagation in gases contained in rigid straight or conical tubes is considered. Under the assumption that the wavelength is much larger than both the boundary layer thickness and the tube radius, pressure and flow are shown to be solutions of a pair of coupled 1D differential equations, formulated as transmission line equations involving complex loss coefficients. The derivation of these loss coefficients, which is usually accomplished in cylinders, is generalized here to conical geometries. In the well-kown case of circular cylinders, the Zwikker–Kosten (ZK) theory is recovered. For circular cones, the expression of the loss coefficients is derived. It involves complex-order spherical harmonics, instead of Bessel functions for circular cylinders, and makes the hydraulic radius appear as a natural relevant geometrical parameter. We show that replacing the classical radius by the hydraulic radius in the ZK theory provides an affordable and accurate approximation of the analytic model derived for cones. The proposed formulas are used to compute the input impedance of a cone, and compared with a 3D reference. In an ideal setting, using the spherical harmonics or the hydraulic radius in the 1D method accurately approximates the full 3D method, and allows to increase accuracy by approximately two orders of magnitude compared to the ZK theory.

2. M2AN

   Construction and convergence analysis of conservative second order local time discretisation for linear wave equations

   Chabassier, Juliette, and Imperiale, Sébastien

   ESAIM: Mathematical Modelling and Numerical Analysis Jul 2021

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   In this work we present and analyse a time discretisation strategy for linear wave equations t hat aims at using locally in space the most adapted time discretisation among a family of implicit or explicit centered second order schemes. The proposed family of schemes is adapted to domain decomposition methods such as the mortar element method. They correspond in that case to local implicit schemes and to local time stepping. We show that, if some regularity properties of the solution are satisfied and if the time step verifies a stability condition, then the family of proposed time discretisations provides, in a strong norm, second order space-time convergence. Finally, we provide 1D and 2D numerical illustrations that confirm the obtained theoretical results and we compare our approach on 1D test cases to other existing local time stepping strategies for wave equations.

3. AA

   Full waveform inversion for bore reconstruction of woodwind-like instruments

   Ernoult, Augustin,  Chabassier, Juliette, Rodriguez, Samuel, and Humeau, Augustin

   Acta Acustica Nov 2021

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   The internal geometry of a wind instrument can be estimated from acoustic measurements. For woodwind instruments, this involves characterizing the inner shape (bore) but also the side holes (dimensions and location). In this study, the geometric parameters are recovered by a gradient-based optimization process, which minimizes the deviation between simulated and measured linear acoustic responses of the resonator for several fingerings through an observable function. The acoustic fields are computed by solving a linear system resulting from the 1D spectral finite elements spatial discretization of the wave propagation equations (including thermo-viscous effects, radiation and side holes). The “full waveform inversion” (FWI) technique exploits the fact that the gradient of the cost function can be computed by solving the same linear system as that of the direct problem but with a different source term. The gradient is computed with better accuracy and less additional cost than with finite-difference. The dependence of the cost function on the choice of the observed quantity, the frequency range and the fingerings used, is first analyzed. Then, the FWI is used to reconstruct, from measured impedances, an elementary instrument with 14 design variables. The results, obtained in about 1 minute on a laptop, are in excellent agreement with the direct geometric measurements.