Beschreibung:
<jats:p>Time-domain simulations are well-suited to study broadband sound propagation. One of the difficulties is the translation of frequency-dependent impedance boundary conditions that leads in the time domain to convolutions. Several methods have been proposed in the literature to have an efficient computation of convolutions. They are based on a multipole approximation of the impedance and on approximations of time-variations of the acoustic variables, allowing the convolution to be simply evaluated by recursive relations. Recently, Dragna et al. [J. Acoust. Soc. Am. 138, 1030–1042 (2015)] have highlighted that recursive convolution methods are low-order methods and have introduced a new method, referred to as the auxiliary differential equation method, which allows one to compute convolutions by integrating in time ordinary differential equations. Its main advantage is that it preserved the order of accuracy. This approach was employed in Troian et al. [J. Sound Vib. 392, 200–216 (2017)] to derive a time-domain impedance boundary condition (TDBIC). This paper aims at evaluating the accuracy and efficiency of this novel TDBIC and to compare it to those of recursive convolution approaches. The novel TDBIC is first presented. A one-dimensional test case, dealing with reflection of an acoustic pulse over an absorbing wall is then investigated. Examples of simulations in three-dimensional geometries in the context of duct acoustics or outdoor sound propagation are then shown.</jats:p>