A time-space decomposition method for calculating the nearfield pressure generated by a pulsed circular piston

Area of Science:

• Acoustics
• Computational Physics
• Numerical Analysis

Background:

• Calculating transient nearfield pressure from circular pistons is crucial for various applications.
• Existing numerical methods, such as Rayleigh-Sommerfeld and Schoch integrals, can be computationally intensive.
• Direct impulse response calculations also face efficiency limitations.

Purpose of the Study:

• To introduce and validate a time-space decomposition approach for efficient transient nearfield pressure calculations.
• To compare the computational speed of the new method against established techniques.

Main Methods:

• Derivation of a time-space decomposition for a single integral expression.
• Analytical separation of temporal and spatial components.
• Conversion of pressure calculations into a superposition of spatial integrals weighted by time-dependent factors.

Main Results:

• Time-space decomposition demonstrated significant speed improvements, being one to two orders of magnitude faster than integral methods and the Field II program.
• Compared to direct impulse response calculations, time-space decomposition was 3x faster for a 10% error and 17x faster for a 1% error.
• The method proved significantly faster for achieving specified maximum error tolerances.

Conclusions:

• The time-space decomposition approach offers a substantial computational advantage for transient nearfield pressure calculations.
• This method provides a more efficient alternative to existing numerical techniques for acoustic modeling.
• The findings suggest broader applicability in fields requiring rapid acoustic simulations.