Reduced basis modelling for accelerated numerical room acoustics simulations

Room acoustic simulations are valuable for designing indoor spaces’ acoustic conditions before construction or renovation. The simulations’ accuracy and efficiency are always compromised but are required in the building industry. This PhD aims to contribute to the field of room acoustic simulations by improving efficiency and accuracy using the reduced basis method (RBM). Numerical discretization methods are able to solve computationally the partial differential equation that describes the wave motion in an enclosure, including all the physics and wave phenomena involved. Thus, simulations are considered accurate as the propagation of the wave is not approximated (except for numerical errors by the discretization), unlike geometrical acoustics (GA) methods. For example, the ray tracing method approximates sound propagation by assuming that sound waves follow the laws of geometrical optics, which is only valid for high frequencies but ensures a manageable computational cost. Thus, it fails to simulate the correct wave nature of sound, e.g., lacking diffraction and interference at low frequencies. However, numerical methods are overly computationally costly when modelling large spaces and/or high frequencies due to the increase of the size of the system of equations that needs to be handled. This drawback makes integrating numerical discretization methods into the building design stages challenging. In this study, the spectral element method (SEM) in the Laplace domain is developed as the high-fidelity solver or full order model (FOM). This high-order numerical scheme possesses valuable qualities required to achieve more efficient room acoustic simulations. The acceleration of the simulations is investigated by introducing a framework that reduces the computational cost compared to the traditional FOM. The framework is based on the RBM, which is derived for room acoustics, including parameterization of key design parameters at the domain’s boundaries. Moreover, it is suitable for the building design procedure where many solutions are required to find the optimal acoustic condition by varying key design parameters. The method consists of a prior stage called the offline stage, where FOM solutions are generated under the variation of the parameters. The set of solutions is utilized to extract basis functions representing the variation of the parameters in the solution. Then, a reduced system of equations called the reduced order model (ROM) can be built by employing a Galerkin projection. Finally, the ROM is used in the so-called online stage to obtain a new parameter value solution at a reduced computational cost. The reduction comes from the truncation of the number of basis modes, which can lead to numerical instability. We avoided such issue by stating the problem in the Laplace domain, as numerical stabilities are ensured for problems described in the frequency domain. It is shown how the proposed reduced basis spectral element method (RB-SEM) can significantly reduce the computational burden. Results show two and three orders of magnitude of acceleration for 2D and 3D cases, respectively, for the investigated cases. Moreover, it is shown how increasing the size of the problem increases acceleration. The method is rigorously analysed for different scenarios, including non-uniform boundary conditions and complex ROMs with a large number of parameters. The compromise between accuracy and speedup is studied in terms of perception. A listening test is conducted to detect the just noticeable difference in the accuracy between the FOM and the ROM. The study concludes with a first understanding of the accuracy requirements in terms of perception for the RBM in room acoustics. Another challenge in the building design is the communication of the acoustic simulation results with non-acousticians. Auditory virtual reality (AVR) can facilitate the communication of the results by providing an immersive visual and auditory experience. A method for generating an AVR experience is proposed. The method is analyzed with subjective tests and applied to real building design cases. Finally, the AVR system is combined with the RB-SEM. A virtual reality (VR) mockup of an existing meeting room is developed, including high-quality visuals and acoustic simulations. A hybrid acoustic simulation method is proposed, where high frequencies are simulated using a GA method, and low frequencies below 1 kHz are simulated using the RB-SEM. Binaural impulse responses are provided by means of spherical harmonic decomposition. Moreover, the VR model allows for change between receiver positions and acoustic conditions. The acoustic conditions are computed using the RBM, where the ROM is constructed by parameterizing the flow resistivity of the acoustic curtains placed at the walls of the room. Results show speedups of 420 without introducing audible differences, where computational times of the magnitude of days can be reduced to minutes.