Time-domain room acoustic simulations with extended-reacting porous absorbers using the discontinuous Galerkin method

This paper presents an equivalent fluid model (EFM) formulation in a three-dimensional time-domain discontinuous Galerkin finite element method framework for room acoustic simulations. Using the EFM allows for the modeling of the extended-reaction (ER) behavior of porous sound absorbers. The EFM is formulated in the numerical framework by using the method of auxiliary differential equations to account for the frequency dependent dissipation of the porous material. The formulation is validated analytically and an excellent agreement with the theory is found. Experimental validation for a single reflection case is also conducted, and it is shown that using the EFM improves the simulation accuracy when modeling a porous material backed by an air cavity as compared to using the local-reaction (LR) approximation. Last, a comparative study of different rooms with different porous absorbers is presented, using different boundary modeling techniques, namely, a LR approximation, a field-incidence (FI) approximation, or modeling the full ER behavior with the EFM. It is shown that using a LR or FI approximation leads to large and perceptually noticeable errors in simulated room acoustic parameters. The average T₂₀ reverberation time error is 4.3 times the just-noticeable-difference (JND) threshold when using LR and 2.9 JND when using FI.