A phenomenological extended-reaction boundary model for time-domain wave-based acoustic simulations under sparse reflection conditions using a wave splitting method

Abstract

In environmental acoustics and in room acoustics, many surfaces exhibit extended-reaction (ER) behavior, i.e., their surface impedance varies with the angle of the incident sound wave. This paper presents a phenomenological method for modeling such angle dependent surface impedance properties in time-domain wave-based simulations. The proposed method has two attractive features: 1) it is general and can be used to model any type of surface as long as the angle dependent surface impedance is known, and 2) it adds little computational cost to the simulation. The method relies on the assumption of a low reflection density, rendering it suitable for modeling, e.g., outdoor sound propagation and early reflections in large rooms. A wave splitting technique is used to separate the reflected wave from the incident wave at the boundary for each time step of the simulation. Once separated, the angle of the incident sound field is determined and the surface impedance adjusted accordingly. The proposed method is validated analytically and experimentally for a single reflection case with different porous sound absorbers. A clear improvement in accuracy is observed, as compared to locally reacting boundary conditions.