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Finite Volume Modeling of Viscothermal Losses and Frequency-Dependent Boundaries in Room Acoustics Simulations

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Wave-based simulation methods for room acoustics applications, whether for purposes of auralisation, or artificial reverberation, offer an increasingly viable alternative to computationally cheaper geometrical acoustics based methods. The advantage is that one has, at least in principle, a means of simulating the entire acoustic field in an enclosure, under minimal simplifying hypotheses. The great difficulty in the design of such methods, through standard techniques such as the finite difference time domain method (FDTD), has been in coping with irregular geometries, as well as nontrivial frequency-dependent wall conditions. Finite volume time domain (FVTD) generalisations of FDTD allow for stable modeling of such complex boundary terminations. An additional feature, and the subject of this paper, is that of viscothermal loss, which plays a major role in room decay times, particularly in the high frequency range. In the present study, 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 for nontrivial room geometries, making use of fitted cells based on the face-centered cubic (FCC) grid.

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