A major design consideration for volumetric wave-based time-domain room acoustics simulation methods, such as finite difference time domain (FDTD) methods, must be sufficiently general, or robust, to handle irregular room geometries and frequency-dependent and spatially varying wall conditions. A general framework for the design of such schemes is presented here, based on the use of the passivity concept, which underpins realistic wall conditions. This analysis is based on the use of conservative finite volume methods, allowing for a representation of the room system as a feedback connection of a lossless part, corresponding to wave propagation over the interior, and a lossy subsystem, representing the effect of wall admittances. Such a representation includes simpler FDTD methods as a special case, and allows for the determination of stability conditions for a variety of time-stepping strategies.

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