MATHICSE Technical Report: Time domain room acoustic simulations using a spectral element method

This paper presents a wave-based numerical scheme based on a spectral element method, coupled with an implicit-explicit Runge-Kutta time stepping method, for simulating room acoustics in the time domain. The scheme has certain features which make it highly attractive for room acoustic simulations, namely a) its low dispersion and dissipation properties due to a high-order spatio-temporal discretization, b) a high degree of geometric flexibility, where adaptive, unstructured meshes with curvilinear mesh elements are supported and c) its suitability for parallel implementation on modern many-core computer hardware. A method for modelling locally reacting, frequency dependent impedance boundary conditions within the scheme is developed, in which the boundary impedance is mapped to a multipole rational function and formulated in differential form. Various numerical experiments are presented, which reveal the accuracy and cost-eciency of the proposed numerical scheme

Modeling extended-reaction boundary conditions in time-domain wave-based simulations of room acoustics

This paper presents a general method for modeling extended-reaction surface impedance boundary conditions in time-domain wave-based room acoustic simulations. A sound field separation technique is used to separate the sound field at a boundary into its incident and reflected components, in each time step of the simulation. Once separated, the incidence angle of the incident sound field is determined and the boundary surface impedance is adjusted accordingly. This allows for the incorporation of angle dependent properties of extended-reaction room surfaces in the simulation. The proposed method is validated both analytically and experimentally. An excellent agreement is found between simulations and analytic and measured reference data. Furthermore, a significant improvement in accuracy is observed, when comparing the extended-reaction model to the commonly used local-reaction model, particularly for surface types which exhibit strong extended-reaction behavior. A room with a suspended porous ceiling is simulated using local- and extended-reaction models, where large and perceptually noticeable differences are found, indicating the importance of including extended-reaction behavior in simulations of room acoustics

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 T-20 reverberation time error is 4.3 times the just-noticeable-difference (JND) threshold when using LR and 2.9 JND when using FI