Local Time-domain Spherical Harmonic Spatial Encoding for Wave-based Acoustic Simulation

Volumetric time-domain simulation methods, such as the finite difference time domain (FDTD) method, allow for a fine-grained representation of the dynamics of the acoustic field. A key feature of such methods is complete access to the computed field, normally represented over a Cartesian grid. Simple solutions to the problem of extracting spatially-encoded signals, necessary in virtual acoustics applications, result. In this article, a simple time domain representation of spatially-encoded spherical harmonic signals is written directly in terms of spatial derivatives of the acoustic field at the receiver location. In a discrete setting, encoded signals may be obtained, at very low computational cost and latency, using local approximations with minimal number of grid points, and avoiding large convolutions and frequency-domain block processing of previous approaches. Numerical results illustrating receiver directivity and computed time domain responses are presented, as well as numerical solution drift associated with repeated time integration.