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A meshless method for unbounded acoustic problems.

Arman Shojaei1, Bijan Boroomand2, Ehsan Soleimanifar2

  • 1Department of Industrial Engineering, University of Padua, Via Venezia 1, 35131 Padova, PD, Italy.

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Summary

This study introduces an effective meshless method for solving acoustic problems on unbounded domains. The approach uses local residual-free basis functions and radiative boundary conditions for accurate simulations.

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Area of Science:

  • Computational physics
  • Acoustics
  • Numerical methods

Background:

  • Solving acoustic wave propagation in unbounded domains presents significant computational challenges.
  • Traditional methods often require domain truncation or complex boundary treatments.
  • Accurate modeling of far-field effects is crucial for realistic acoustic simulations.

Purpose of the Study:

  • To propose an effective meshless method for solving time-harmonic acoustic problems on unbounded domains.
  • To accurately incorporate far-field effects using radiative boundary conditions.
  • To validate the proposed method through numerical acoustic problem-solving.

Main Methods:

  • Discretization of the near field using nodes and local residual-free basis functions on finite clouds.
  • Incorporation of far-field effects via radiative boundary conditions and residual-free bases on infinite clouds.
  • Satisfaction of radiation conditions by the basis functions in the far field.

Main Results:

  • The proposed meshless method effectively handles acoustic problems on unbounded domains.
  • Accurate approximation of both near-field and far-field behavior is achieved.
  • Validation through solving representative acoustic problems confirms the method's efficacy.

Conclusions:

  • The developed meshless method offers an efficient and accurate solution for time-harmonic acoustic problems.
  • The use of local residual-free basis functions and radiative boundary conditions is a viable strategy for unbounded domain problems.
  • This method provides a robust tool for computational acoustics research and applications.