In room acoustics simulation and virtualization applications, accurate wall termination is a perceptually crucial feature. It is particularly important in the setting of wave-based modeling of 3D spaces, using methods such as the finite difference time domain method or finite volume time domain method. In this paper, general locally reactive impedance boundary conditions are incorporated into a 3D finite volume time domain formulation, which may be specialized to the various types of finite difference time domain method under fitted boundary termination. Energy methods are used to determine stability conditions for general room geometries, under a large family of nontrivial wall impedances, for finite volume methods over unstructured grids. Simulation results are presented, highlighting in particular the need for unstructured or fitted cells at the room boundary in the case of the accurate simulation of frequency-dependent room mode decay times.

Finite difference solutions to the wave equation are simple and flexible modeling tools for approximating physical systems in audio and room acoustics. Each model is characterized by a matrix operator and the time-stepping solution by a sequence of powers of the matrix. Spectral decomposition of representative matrices provide some practical insight into solution behavior and in some cases stability. In addition to computed eigenvalue spectra, pseudospectra provide a description of numerical amplification due to rounding errors in floating point arithmetic. The matrix analysis also shows that certain boundary implementations in non-cuboid geometries can be unstable despite satisfying conditions derived from von Neumann and normal mode analyses.

Room acoustic simulation is the process of generating approximate solutions to either the linearized Euler equations or the scalar wave equation. As for the continuous equations, the discrete approximations of both are equivalent. The vector formulation is less efficient, but it can inform several unexploited features of the scalar formulation. This paper first demonstrates the equivalence of the two schemes and explores how the vector formulation may be integrated into the more efficient scalar formulation to produce local velocity estimates and velocity sources on the pressure grid.

Bayesian model selection and parameter estimation are used to address the problem of choosing the most concise filter order for a given application while simultaneously determining the associated filter coefficients. This approach is validated against simulated data and used to generate pole-zero representations of head-related transfer functions.