Room Acoustic Simulations using High-Order Spectral Element Methods Finnur Pind 1,2 , Mikael Staugaard Mejling 3 , Allan P. Engsig-Karup 3 , Cheol-Ho Jeong 2 , Jakob Strømann-Andersen 1 1) Henning Larsen, Copenhagen, Denmark. 2) Acoustic Technology group, Department of Electrical Engineering, Technical University of Den- mark, Lyngby, Denmark. 3) Scientific Computing group, Department of Applied Mathematics and Computer Science, Technical University of Denmark, Lyngby, Denmark. Summary A wave-based numerical scheme for simulating room acoustics, based on the spectral element method, is presented. This method possesses qualities, such as high-order accuracy and geometrical flexibility, which make it very suitable for accurate and cost-effective room acoustic simulations of complex geometries of any size and shape. Various numerical experiments are carried out in order to analyze the accuracy and efficiency of the scheme. The results demonstrate how using high-order elements is essential for capturing wave dispersion and thereby allowing for the usage of coarser spatial dis- cretizations, which can reduce computation time significantly. Furthermore, the methods ability to accurately represent curved boundaries, by means of curvilinear mesh elements, is demonstrated. The investigation is relevant for understanding how to improve the accuracy of room acoustics sim- ulations in real geometries and serves as a stepping stone towards developing a relatively fast and flexible wave-based room acoustic simulator. PACS no. 43.55.Ka, 43.58.Ta 1. Introduction The subject of computer simulations of room acous- tics dates back to the 1960’s [1, 2] and since the 1990’s, commercial software for room acoustic simula- tions has been readily available [3]. Since the acoustic performance of almost all real rooms is difficult or almost impossible to predict with sufficient accuracy without resorting to computer simulations, these soft- ware packages have become essential tools for most practicing room acousticians and other building de- signers involved with room acoustics [4]. The algorithms which are used for simulating acous- tic sound propagation and reflection within rooms are typically divided into two main categories, namely the “geometrical” approach and “wave-based” approach. Examples of geometrical methods include the ray tracing method [5], the image source method [6] and the beam tracing method [7]. Geometrical algorithms are usually relatively fast, but the accuracy is often insufficient [8]. Particularly, in cases where wave phe- nomena, such as diffraction, interference, phase and (c) European Acoustics Association scattering are a prominent part of the acoustic re- sponse of the room. Diffraction, [perceptually notice- able] interference and phase will mainly arise in small and medium sized spaces, and at low-mid frequen- cies. However, there are also well known cases of large spaces where geometrical methods cannot account for certain acoustic phenomena, such as the seat-dip ef- fect [9] and in cases where acoustic focusing is promi- nent [10]. Most room acoustic software which use ge- ometrical methods have some methods to account for surface scattering. Here the room surfaces are usually assigned scattering coefficients, but typically these co- efficients are guesstimated based on crude visual in- spections. There is still ongoing active research and development of geometrical algorithms, see [11, 12, 13] for examples of discussions of state of the art geomet- rical room acoustic algorithms. Wave-based methods solve the governing acoustical equations numerically, usually either the wave equa- tion or the equivalent linearized Euler equations. By solving the acoustical equations directly, all acoustic phenomena are inherently accounted for and these methods therefore allow for greater accuracy than their geometrical counterparts [8]. The drawback is that these methods come with a much higher com- putational cost than the geometrical methods. Exam- Copyright © 2018 | EAA – HELINA | ISSN: 2226-5147 All rights reserved - 2085 -