Time domain wave-based methods sidestep the consequences of the simplifying hypotheses that are part of geometric ray-based methods when simulating, modeling, and analyzing room acoustics. This paper illustrates construction techniques for wave-based simulation methods when applied to nontrivial problems in room acoustics, including irregular geometries and frequency-dependent boundary conditions, which are extended to include viscothermal loss effects in air. However, algorithm design has many challenges when applied to realistic room con?gurations. The main design criteria are arbitrary room geometry, general passive frequency-dependent and spatially-varying wall conditions, and adequate modeling of viscothermal and relaxation effects. The main difficulty is the construction of simulation methods that are numerically stable. Finite volume time domain (FVTD) methods generalize certain ?nite difference time domain (FDTD) methods, while allowing for stability analysis. FVTD methods with frequency-dependent impedance boundary conditions are extended to handle such viscothermal loss effects in air. An energy-based analysis of numerical stability is presented in detail, illustrating conditionally and unconditionally stable forms that are extended to cover the case of dissipation through a time-integrated energy balance.
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