High order local absorbing boundary conditions for acoustic waves in terms of farfield expansions

JOURNAL OF COMPUTATIONAL PHYSICS

卷:333

Article

Villamizar, Vianey¹  Acosta, Sebastian²  Dastrup, Blake¹ 

[1] Brigham Young Univ, Dept Math, Provo, UT 84602 USA

[2] Baylor Coll Med, Dept Pediat Cardiol, Houston, TX 77030 USA

关键词: Acoustic scattering;    Nonreflecting boundary condition;    High order absorbing boundary condition;    Helmholtz equation;    Farfield pattern;   

DOI  :  10.1016/j.jcp.2016.12.048

来源: Elsevier

【 摘 要 】

We devise a new high order local absorbing boundary condition (ABC) for radiating problems and scattering of time-harmonic acoustic waves from obstacles of,arbitrary shape. By introducing an artificial boundary S enclosing the scatterer, the original unbounded domain Omega is decomposed into a bounded computational domain Omega(-) and an exterior unbounded domain Omega(+). Then, we define interface conditions at the artificial boundary S, from truncated versions of the well-known Wilcox and Karp farfield expansion representations of the exact solution in the exterior region Omega(+). As a result, we obtain a new local absorbing boundary condition (ABC) for a bounded problem on Omega(-), which effectively accounts for the outgoing behavior of the scattered field. Contrary to the low order absorbing conditions previously defined, the error at the artificial boundary induced by this novel ABC can be easily reduced to reach any accuracy within the limits of the computational resources. We accomplish this by simply adding as many terms as needed to the truncated farfield expansions of Wilcox or Karp. The convergence of these expansions guarantees that the order of approximation of the new ABC can be increased arbitrarily without having to enlarge the radius of the artificial boundary. We include numerical results in two and three dimensions which demonstrate the improved accuracy and simplicity of this new formulation when compared to other absorbing boundary conditions. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free