Treatment of frequency-dependent admittance boundary conditions in transient acoustic finite/infinite-element models.

The paper addresses the handling of frequency-dependent, local admittance boundary conditions in acoustic transient finite/infinite-element models. The proposed approach avoids the evaluation of a convolution integral along the related boundary. Based on a similar technique developed in an aeroacoustic/finite difference context, the spatially local boundary condition is rewritten in a discrete form that involves normal accelerations and pressure time derivatives at the current time step and few steps before. The incorporation of such a discrete (in time) boundary condition in a finite/infinite-element context is addressed. The infinite-element scheme selected for that purpose relies on the conjugated Astley-Leis formulation. Implementation aspects cover the handling of frequency-dependent boundary conditions along both finite- and infinite-element edges. Numerical examples (waveguide, single source in a half-space bounded by an impedance plane, diffraction by an acoustically treated screen) are presented in order to demonstrate the efficiency of the proposed approach.