Radiosity and radiative transfer in sound and vibration

At high frequencies in acoustics, the most popular method is ray-tracing and its variants including radiosity. In structural vibrations, the most known method is rather statistical energy analysis [1]. Both methods may be derived from a unique approach based on radiative transfer equations analogous to radiative exchanges of energy in thermics [2]. In this study, we present an overview of the radiative transfer equations in sound and vibration. We first show that radiosity is equivalent to ray-tracing with Lambertian reflection. In steady-state condition, radiosity is strictly equivalent to the view factor method in thermics. But in transient condition, radiosity provides an elegant solution to predict reverberation beyond the validity of Sabine's law. The theory is also well suited for structural rays in built-up structures. The radiative transfer equations account for reflection and transmission at interfaces of structural components. Sound radiation may also be described in the limit of high frequencie...