Passive time-domain numerical designs for room acoustics simulation

The design of stable time domain numerical simulation methods for room acoustics simulation is challenging problem. One chief difficulty is in the determination of appropriate stable boundary terminations, particularly when the room geometry is irregular, and when the wall condition is spatially-varying and/or frequency-dependent in a non-trivial way. In this paper, design strategies for stable simulation are presented, based on the finite volume time domain method (FVTD), which, due to its unstructured character, allows for flexible modelling of irregular room geometries.
Furthermore, FVTD reduces to the popular finite difference time domain (FDTD) method under certain choices of regular structured mesh. Under locally-reactive wall conditions, the boundary condition can be characterised by a positive real admittance function, variable over the extent of the room boundary. Using frequency-domain analysis techniques, it can be shown that solutions to the complete system are non-increasing. Furthermore, such analysis techniques can
be extended to the case of discrete time simulations, leading to numerical stability conditions for a complete room simulation. Distinct explicit and implicit time-domain simulation methods are analysed in this manner. Extensions to the case of non-locally reactive conditions are discussed.