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.

Modal Representation of the Resonant Body within a Finite Difference Framework for Simulation of String Instruments

This paper investigates numerical simulation of a string coupled
transversely to a resonant body. Starting from a complete nite
difference formulation, a second model is derived in which the
body is represented in modal form. The main advantage of this hybrid form is that the body model is scalable, i.e. the computational
complexity can be adjusted to the available processing power. Numerical results are calculated and discussed for simplied models
in the form of string-string coupling and string-plate coupling.

An Energy Conserving Finite Difference Scheme for Simulation of Collisions

Nonlinear phenomena play an essential role in the sound production process of many musical instruments. A common source of these effects is object collision, the numerical simulation of which is known to give rise to stability
issues. This paper presents a method to construct numerical schemes that conserve the total energy in simulations of one-mass systems involving collisions, with no conditions imposed on any of the physical or numerical parameters.
This facilitates the adaptation of numerical models to experimental data, and allows a more free parameter adjustment in sound synthesis explorations. The energy preservedness of the proposed method is tested and demonstrated though several examples, including a bouncing ball and a non-linear oscillator, and implications regarding the wider applicability are discussed.

A Spherical Array Approach for Simulation of Binaural Impulse Responses using the Finite Difference Time Domain Method

The finite difference time domain (FDTD) method has direct applications in musical instrument modeling, simulation of environmental acoustics, room acoustics and sound reproduction paradigms, all of which benefit from auralization. However, rendering binaural impulse responses from simulated
data is not straightforward to accomplish as the calculated pressure at FDTD grid nodes does not contain any directional information. This paper addresses this issue by introducing a spherical array to capture sound pressure on a finite difference grid, and decomposing it into a plane-wave density
function. Binaural impulse responses are then constructed in the spherical harmonics domain by combining the decomposed grid data with free field head-related transfer functions. The effects of designing a spherical array in a Cartesian grid are studied, and emphasis is given to the relationships
between array sampling and the spatial and spectral design parameters of several finite-difference
schemes.

Binaural Reproduction of Finite Difference Simulations Using Spherical Array Processing

Due to its efficiency and simplicity, the finite-difference time-domain method is becoming a popular choice for solving wideband, transient problems in various fields of acoustics. So far, the issue of extracting a binaural response from finite difference simulations has only been discussed in the context of embedding a listener geometry in the grid. In this paper, we propose and study a method for binaural response rendering based on a spatial decomposition of the sound field. The finite difference grid is locally sampled using a volumetric array of receivers, from which a plane wave density function is computed and integrated with free-field head related transfer functions, in the spherical harmonics domain. The volumetric array is studied in terms of numerical robustness and spatial aliasing. Analytic formulas that predict the performance of the array are developed, facilitating spatial resolution analysis and numerical binaural response analysis for a number of finite difference schemes. Particular emphasis is placed on the effects of numerical dispersion on array processing and on the resulting binaural responses. Our method is compared to a binaural simulation based on the image method. Results indicate good spatial and temporal agreement between the two methods.