Numerical modelling of sound radiation and transmission in buildings using the time-domain nodal discontinuous Galerkin method

This study presents numerical solutions for two vibroacoustic problems using the time-domain nodal discontinuous Galerkin (DG) method. The first problem is the impact sound radiation from a rectangular slab into a cuboid room, and the second is the sound transmission between two cuboid rooms with direct and flanking contributions. The structures are modelled as a three-dimensional solid governed by the linear elasticity equations, and sound propagation in the rooms is governed by the linear acoustic equations. In the impact sound radiation case, the normalised sound pressure is evaluated and compared to the one obtained by the modal expansion method. In the sound transmission case, pressure transfer functions between different positions are calculated and compared to those obtained by the finite element method (FEM). The upwind numerical fluxes in DG for both governing equations, as well as the coupling conditions, are presented. There is excellent agreement between the solutions obtained by the nodal DG and those obtained by the modal expansion method/FEM. Although minor discrepancies exist in the resonance frequencies and magnitude, the overall trend shows good agreement.