Wave-Based Room Acoustics Simulation: Explicit/Implicit Finite Volume Modeling of Viscothermal Losses and Frequency-Dependent Boundaries

Time domain wave-based methods sidestep the simplifying hypotheses underlying geometric (ray-based) methods and offer, in theory, a complete solution to the problem of room acoustics simulation. Many issues remain at the level of algorithm design, particularly under realistic room configurations. The main design criteria are: (a) arbitrary room geometry, (b) general passive frequency-dependent and spatially-varying wall conditions, and (c) adequate modeling of viscothermal and relaxation effects. The third feature, which is the focus of this article, plays a major role in room decay times, particularly in the high frequency range. The main difficulty, under such general conditions, is in the construction of simulation methods that are numerically stable. Finite volume time domain (FVTD) methods generalize certain finite difference time domain (FDTD) methods, while allowing for such stability analysis. Here, FVTD methods under frequency-dependent impedance boundary conditions are extended to handle such viscothermal effects with an implicit/explicit time integration scheme, while allowing for a means of terminating a numerical method in a stable manner. An energy based analysis of numerical stability is presented here in detail, leading to conditionally and unconditionally stable forms, and extended to cover the case of dissipation through a time integrated energy balance. Simulation results are presented.