Construction and validation of a broadband time domain impedance boundary condition

Time domain simulations are suited to predict acoustic propagation problems, which can handle the broadband and nonlinear acoustic problems relatively easily. An improved multipole broadband impedance model for sound propagation over impedance surfaces is proposed, and the corresponding time domain impedance boundary condition is presented. Basing on the three-parameter model, the multi-pole impedance model was constructed through combing with a series of complex conjugate pole-residue pairs functions. The impedance boundary condition can be implemented into a computational aeroacoustics solver by a recursive convolution technique, which results in a fast and computationally efficient algorithm. Analytical solutions for broadband acoustic propagation benchmark problems both in one dimension and two dimensions are derived and used to validate the proposed time domain impedance boundary condition. To be further validated, numerical simulations are performed by calculating the NASA grazing incidence tube with multifrequency input waves. The good agreement shows that the proposed time-domain impedance boundary condition is accurate and the method of implementation is efficient for solving broadband sound propagation problems with impedance surfaces.