Numerical methods for wave scattering phenomena by means of different boundary integral formulations

Bodo Nolte, Ingo SchÄfer, Jan Ehrlich, Martin Ochmann, Ralf Burgschweiger, Steffen Marburg

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

Different numerical approaches for the physical phenomena of scattering waves from an obstacle are presented. They are based on different integral formulations. Fluid structure interaction effects are numerically treatable as well. We use the Boundary Element Method (BEM) in different approaches because the inherently satisfied Sommerfeld radiation condition makes sure that no reflecting waves from boundaries at infinity occur. One of the biggest disadvantages of numerical methods like BEM is the fact that they have difficulties with handling the high frequency range. For the high frequency range approximations like the Kirchhoff-Helmholtz integral equation have to be used. With varying assumptions of the reflecting behavior of the structure different approaches for the higher frequency range are obtained, where the explicit solving of a system of equations is not necessary. Another high frequency approach is the plane wave approximation which is compared with the Kirchhoff approach of the first kind. Additionally a modified Kirchhoff approach is introduced. Because the incident pressure on the scatterer's surface is known the integral is evaluated analytically on triangular patches. The discretization is no longer frequency dependent and the size of the patches only depends on the curvature of the structure. Large planar parts can be discretized with one element only. This leads to a substantial advantage in terms of calculation time over the traditional Kirchhoff approach. Like the traditional approach this procedure is valid under the assumption of high frequency or far field conditions.

Original languageEnglish
Pages (from-to)495-529
Number of pages35
JournalJournal of Computational Acoustics
Volume15
Issue number4
DOIs
StatePublished - Dec 2007
Externally publishedYes

Keywords

  • Boundary element method
  • Double scattering
  • Kirchhoff approaches of different orders
  • Modified Kirchhoff
  • Multiple scattering
  • Plane wave approximation
  • Target strength

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