ADITU: A mesh-free formulation for the solution of Helmholtz equation in bounded and unbounded domains

Abstract

This work describes a mesh-free collocation formulation for the acoustic fluid–fluid coupling among non-homogeneous bounded and unbounded fluid domains. The proposed formulations use series of functions that are generated using the analytical solutions of Helmholtz equation in spherical coordinates, and coefficients of the series are calculated from applying the boundary conditions. The technique is able to calculate the acoustic pressure in any bounded or unbounded non-spherical domain. The accuracy, efficiency and robustness of the model is tested by using as benchmark classical analytic solutions of radiation and scattering from spheres.

Keywords

• Helmholtz equation
• Acoustic radiation
• Acoustic scattering
• Unbounded domains
• Fluid–fluid coupling