Spectral approaches for room acoustical simulation

Simple techniques for predicting sound pressure levels in closed volumes for steady state excitation are typically based on averaging methods like the Statistical Energy Analysis. They give robust results for subsystems with high modal density, if the averaging over frequency bands, points of excitation and points of observation is carried out. For predicting the spatial resolution of the response, especially for calculating impulse response functions of systems with complicated boundary conditions, often Finite Element approaches are used. For the simulation of large systems in the middle and higher frequency range the number of unknowns increases rapidly. Therefore Spectral Methods and Spectral Element Methods (SEM) and their characteristic p- or hp-refinement are used in order to decrease the degrees of freedom while preserving the accuracy compared to the linear Finite Element Method (LFEM). Considering the fact, that for many applications a limited frequency range is of interest, a systematic procedure to calculate frequency-response functions and - in a second step - impulse response functions by means of SEM is applied in the presented work. The method is based on a modal approach for the fluid using the component mode synthesis to reduce the effort of computation (especially for optimization problems). Free interface eigenmodes or wave-number approaches are used at the coupling interface to model the deformation pattern (attachment modes). In addition, focus is laid on the description of various absorbers, modeled by the help of the Theory of Porous Media. The method is presented and models of the decoupled components are shown for practical acoustic boundary conditions and realistic acoustic cavities, where analytical and numerical methods (Finite Elements, Spectral Methods and Spectral Elements) are used.