Incorporating directivity in the Fourier pseudospectral time-domain method using spherical harmonics

Area of Science:

• Computational physics
• Acoustic modeling
• Numerical methods

Background:

• Accurate acoustic modeling requires incorporating source and head-related directivity.
• The pseudospectral time-domain method (PSTD) is an efficient technique for solving linear acoustics equations.
• Implementing directive sources in PSTD is crucial for realistic sound field simulations.

Purpose of the Study:

• To implement directive sources within the pseudospectral time-domain method (PSTD).
• To enable accurate acoustic modeling and auralization by including frequency-dependent source directivity.
• To validate the implemented method against analytical models.

Main Methods:

• Decomposition of frequency-dependent source directivity onto spherical harmonic functions.
• Implementation of directive sources in PSTD using spatial distributions related to spherical harmonics.
• Assignment of time-dependent functions to spatial distributions to represent directivity's frequency content.

Main Results:

• Successful modeling of an analytically designed directivity function in PSTD.
• Good agreement between analytical and simulated directivity shown by octave band analysis.
• Acceptable distance-related error (<0.9 dB) observed beyond 17.5 grid cells from the source.

Conclusions:

• The proposed method effectively models any directive source by leveraging spherical harmonic decomposition.
• PSTD with implemented directive sources provides accurate acoustic simulations for modeling and auralization.
• The method demonstrates good accuracy for practical simulation distances.