Computational Accuracy and Efficiency of Room Acoustics Simulation Using a Frequency Domain FEM with Air Absorption: 2D Study

Abstract

Recently, to simulate sound propagation inside architectural spaces at high frequencies, the application of computationally expensive wave-based numerical methods to room acoustics simulation is increasing gradually. Generally, standard room acoustics simulations in the frequency domain are performed based on the lossless Helmholtz equation. However, for acoustics simulation at high frequencies, consideration of the sound attenuation effect caused by air absorption is an aspect to increase the reliability of predictions. Although a simple approach based on the lossy Helmholtz equation is available to include the air absorption effect in the frequency domain, its accuracy and efficiency are still not discussed well. This paper presents an accuracy and efficiency estimation of FEM based on the lossy Helmholtz equation via two numerical problems in two dimensions: a plane wave propagation problem up to 20 kHz in a long duct with 1 km length and a sound propagation problem in a real-scale office up to 6 kHz. Results revealed that the lossy Helmholtz equation-based FEM can include the air absorption effect accurately up to 20 kHz. Moreover, a possibility of providing a higher computational efficiency at higher frequencies is suggested when the magnitude of the pure-tone sound attenuation coefficient is large.

Keywords

• air absorption
• complex wave number
• finite element method
• lossy Helmholtz equation
• frequency domain
• room acoustics simulation