Modeling Frequency-Dependent Boundaries as Digital Impedance Filters in FDTD and K-DWM Room Acoustics Simulations

A new method for modeling-frequency-dependent boundaries in finite-difference time-domain (FDTD) and Kirchhoff variable digital waveguide mesh (K-DWM) room acoustics simulations is presented. The proposed approach allows the direct incorporation of a digital impedance filter (DIF) in the Multidimensional (2D or 3D) FDTD boundary model of a locally reacting surface. An explicit boundary update equation is obtained by carefully constructing a Suitable recursive formulation. The method is analyzed in terms of pressure wave reflectance for different wall impedance filters and angles of incidence. Results obtained from numerical experiments confirm the high accuracy of the proposed digital impedance filter boundary model, the reflectance of which matches locally reacting surface (LRS) theory closely. Furthermore a numerical boundary analysis (NBA) formula is provided as a technique for an analytic evaluation of the numerical reflectance of the proposed digital impedance filter boundary formulation.

Wideband and Isotropic Room Acoustics Simulation Using 2-D Interpolated FDTD Schemes

In this paper, a complete method for finite-difference time-domain modeling of rooms in 2-D using compact explicit schemes is presented. A family of interpolated schemes using a rectilinear, nonstaggered grid is reviewed, and the most accurate and isotropic schemes are identified. Frequency-dependent boundaries are modeled using a digital impedance filter formulation that is consistent with locally reacting surface theory. A structurally stable and efficient boundary formulation is constructed by carefully combining the boundary condition with the interpolated scheme. An analytic prediction formula for the effective numerical reflectance is given, and a stability proof provided. The results indicate that the identified accurate and isotropic schemes are also very accurate in terms of numerical boundary reflectance, and outperform directly related methods such as Yee's scheme and the standard digital waveguide mesh. In addition, one particular scheme-referred to here as the interpolated wideband scheme-is suggested as the best scheme for most applications.

Room acoustics simulation using 3-D compact explicit FDTD schemes

This paper presents methods for simulating room acoustics using the finite-difference time-domain (FDTD) technique, focusing on boundary and medium modeling. A family of nonstaggered 3-D compact explicit FDTD schemes is analyzed in terms of stability, accuracy, and computational efficiency, and the most accurate and isotropic schemes based on a rectilinear grid are identified. A frequency-dependent boundary model that is consistent with locally reacting surface theory is also presented, in which the wall impedance is represented with a digital filter. For boundaries, accuracy in numerical reflection is analyzed and a stability proof is provided. The results indicate that the proposed 3-D interpolated wideband and isotropic schemes outperform directly related techniques based on Yee's staggered grid and standard digital waveguide mesh, and that the boundary formulations generally have properties that are similar to that of the basic scheme used.

A Phase Grating Approach to Modeling Surface Diffusion in FDTD Room Acoustics Simulations

In this paper, a method for modeling diffusive boundaries in finite difference time domain (FDTD) room acoustics simulations with the use of impedance filters is presented. The proposed technique is based on the concept of phase grating diffusers, and realized by designing boundary impedance filters from normal-incidence reflection filters with added delay. These added delays, that correspond to the diffuser well depths, are varied across the boundary surface, and implemented using Thiran allpass filters. The proposed method for simulating sound scattering is suitable for modeling high frequency diffusion caused by small variations in surface roughness and, more generally, diffusers characterized by narrow wells with infinitely thin separators. This concept is also applicable to other wave-based modeling techniques. The approach is validated by comparing numerical results for Schroeder diffusers to measured data. In addition, it is proposed that irregular surfaces are modeled by shaping them with Brownian noise, giving good control over the sound scattering properties of the simulated boundary through two parameters, namely the spectral density exponent and the maximum well depth.

Physical and numerical constraints in source modeling for finite difference simulation of room acoustics

In finite difference time domain simulation of room acoustics, source functions are subject to various constraints. These depend on the way sources are injected into the grid and on the chosen parameters of the numerical scheme being used. This paper addresses the issue of selecting and designing sources for finite difference simulation, by first reviewing associated aims and constraints, and evaluating existing source models against these criteria. The process of exciting a model is generalized by introducing a system of three cascaded filters, respectively, characterizing the driving pulse, the source mechanics, and the injection of the resulting source function into the grid. It is shown that hard, soft, and transparent sources can be seen as special cases within this unified approach. Starting from the mechanics of a small pulsating sphere, a parametric source model is formulated by specifying suitable filters. This physically constrained source model is numerically consistent, does not scatter incoming waves, and is free from zero- and low-frequency artifacts. Simulation results are employed for comparison with existing source formulations in terms of meeting the spectral and temporal requirements on the outward propagating wave.