Broadband time-domain impedance boundary modeling with the discontinuous Galerkin method for room acoustics simulations

The time-domain nodal discontinuous Galerkin (TD-DG) method is emerging as a potential wave-based method for three-dimensional (3D) room acoustics modeling, where high-order accuracy, geometrical flexibility and accurate modeling of boundary conditions are of critical importance. In this work, an accurate and efficient formulation of broadband time-domain impedance boundary conditions of locally-reacting surfaces is proposed in the framework of the TD-DG method. The formulation of the time-domain boundary condition is based on the plane-wave reflection coefficient at normal incidence and its approximation in the frequency domain using a sum of rational fractions, which can be obtained from analytical models or measured impedance values. To verify the performance of the formulation, a single reflection scenario is considered and the reflection coefficient obtained from the numerical tests is compared with the analytical one based on a locally reacting surface impedance. Also, the effects of the coefficients of rational functions on the accuracy are investigated. The broadband time-domain impedance boundary formulation accurately predicts both the amplitude and the phase of the reflection behaviour.