Time-Domain Boundary Element Method with Broadband Impedance Boundary Condition

Acoustic liners are an effective tool for noise reduction and are characterized by a frequency-dependent impedance value. In this paper, a time-domain boundary element method for acoustic scattering coupled with a broadband impedance boundary condition is studied for the case of no mean flow. A Burton-Miller reformulation of the time domain boundary element method for acoustic scattering is carried out with both the pressure and its surface normal derivative terms retained. A multipole impedance model is converted into the time domain and used for enforcing an impedance boundary condition over a wide range of frequencies. Discretization of the coupled system is described. In particular, the time-domain impedance boundary condition is discretized by the third-order implicit backward difference scheme. Stability of the coupling is assessed by an eigenvalue analysis. Scattering solutions that demonstrate the validity and stability of the numerical method are presented.