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Exact solutions for transient spherical radiation.

J A Hamilton1, R J Astley

  • 1Department of Mechanical Engineering, University of Canterbury, Christchurch, New Zealand.

The Journal of the Acoustical Society of America
|June 2, 2001
PubMed
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Researchers derived analytic solutions for exterior wave fields from moving spherical boundaries. These benchmark solutions aid in validating transient numerical methods for wave propagation studies.

Area of Science:

  • Acoustics
  • Wave Propagation
  • Computational Physics

Background:

  • Numerical methods for wave propagation require accurate benchmarks.
  • Transient wave fields from complex geometries are challenging to model analytically.

Purpose of the Study:

  • To derive closed-form analytic solutions for exterior wave fields.
  • To provide benchmark problems for transient numerical schemes.
  • To present a novel solution for a spherical piston in a baffle.

Main Methods:

  • Classical Laplace transform methods.
  • Superposition for composite solutions.
  • Detailed derivation for multipoles up to order 25.

Main Results:

Related Experiment Videos

  • Analytic solutions for transient, axisymmetric spherical boundary motion.
  • A novel composite solution for a spherical piston.
  • Consistency with steady-state and numerical solutions.

    • Conclusions:

    • The derived analytic solutions serve as valuable benchmarks.
    • The methods allow for detailed reconstruction and extension.
    • The solutions validate transient numerical schemes.