An adjoint-based method for liner impedance eduction: Validation and numerical investigation

An inverse method for liner acoustic impedance eduction in a duct is presented. The determination of adjoint equations allows to make explicit the directional derivatives of the objective function, needed by the search algorithm. Direct and adjoint system of equations are spatially discretized by a discontinuous Galerkin scheme. The propagation model and the eduction process are successfully validated on NASA benchmark data extracted from literature, in a no-flow configuration. Objective functions written in terms of acoustic pressure and acoustic velocity are considered successively. Special attention is given to the possibilities offered by the method, such as multiparameter identification, with the study of a non-homogeneous liner. Convergence history of the process is also examined, revealing interesting properties for the velocity-based objective function compared to the pressure-based objective function. In further developments, the method is planned to be used with acoustic velocity fields obtained by laser doppler velocimetry.