Boundary-conforming coordinates with grid line control for acoustic scattering from complexly shaped obstacles
✍ Scribed by Vianey Villamizar; Matthew Weber
- Publisher
- John Wiley and Sons
- Year
- 2007
- Tongue
- English
- Weight
- 576 KB
- Volume
- 23
- Category
- Article
- ISSN
- 0749-159X
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✦ Synopsis
Abstract
The current work sets forth a practical approach to numerically solve two‐dimensional direct acoustic scattering problems from complexly shaped scatterers with severe singularities, such as corners and cusps. First, boundary conforming coordinates are generated. This generation is performed through an elliptic grid generator algorithm, including control of the coordinate lines. The grid line control solely depends on the initial distribution of grid points. Following the grid generation process, the initial boundary value problem, modelling the scattering phenomenon, is formulated in terms of the new curvilinear coordinates, and a finite‐difference time domain method is implemented. The presence of the boundary singularities causes instability of the numerical method. However, by appropriately controlling the distance between grid lines in the vicinity of these singularities, stability and convergence are achieved. A semianalytical formula for the differential scattering cross‐section is obtained from the discrete Fourier transform of the computed scattered pressure field. The method is successfully applied to several interesting scatterers of various shapes. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007