Generic and broadband non-linear time domain impedance boundary condition

An approach for modeling time-domain impedance boundary conditions (TDIBC) is presented. Its implementation in numerical codes relies on the inverse Fourier transform to recast the convolution problem into an array rolling operation. The proposed approach offers several advantages, including an inherently broadband formulation that can handle discontinuous waves, the ability to cater for any impedance law on frequency, ease of extension to non-linear impedance operators, and the elimination of ad-hoc, previously-tuned parameters. The linear solver, whose code is shared, is first validated against theoretical results. The non-linear solver is then validated against experimental data obtained in an impedance tube setting. Finally, a fully non-linear Navier-Stokes solver based on discontinuous spectral differences is utilized to demonstrate the implementation of the TDIBC in a grazing incidence duct configuration.