Abstract
All acoustic sources are of finite spatial extent. In volumetric wave-based simulation approaches (including, e.g., the finite difference time domain method among many others), a direct approach is to represent such continuous source distributions in terms of a collection of point-like sources at grid locations. Such a representation requires interpolation over the grid and leads to common staircasing effects, particularly under rotation or translation of the distribution. In this article, a different representation is shown, based on a spherical harmonic representation of a given distribution. The source itself is decoupled from any particular arrangement of grid points, and is compactly represented as a series of filter responses used to drive a canonical set of source terms, each activating a given spherical harmonic directivity pattern. Such filter responses are derived for a variety of commonly encountered distributions. Simulation results are presented, illustrating various features of such a representation, including convergence, behaviour under rotation, the extension to the time varying case, and differences in computational cost relative to standard grid-based source representations.
Highlights
The emulation of sources in time domain wavebased virtual and architectural acoustics has a long history8–13, and follows even earlier work on the representation of sources in electromagnetic simulation14
The implementation of sources with directivity in time domain wave-based acoustics has been explored by various authors
Source directivity modeling using spherical harmonic representations has been been employed in wave-based methods, using pseudospectral time domain methods7, and using FDTD21, leading to a very sparse representation of the source in terms of a canonical set of spherical harmonic difference operators and low order finite impulse response filters
Summary
The emulation of sources in time domain wavebased virtual and architectural acoustics (such as the finite difference time domain method or FDTD1–3, finite volume methods, finite element methods and other varieties7) has a long history, and follows even earlier work on the representation of sources in electromagnetic simulation. Source directivity modeling using spherical harmonic representations has been been employed in wave-based methods, using pseudospectral time domain methods, and using FDTD21, leading to a very sparse representation of the source in terms of a canonical set of spherical harmonic difference operators and low order finite impulse response filters. / 2 December 2020 harmonic formulation is employed, allowing the condensation of an arbitrary source distribution to a point-like directional source that can be implemented directly in the time domain. Such an approach follows from a timedependent multipole representation, and is related to the multipole moment condensation method.
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