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Math. Comput. Appl. 2017, 22(1), 26; doi:10.3390/mca22010026

Modeling Sound Propagation Using the Corrective Smoothed Particle Method with an Acoustic Boundary Treatment Technique

1,2
,
3
and
1,*
1
School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
2
School of Transportation, Wuhan University of Technology, Wuhan 430063, China
3
Wuhan Second Ship Design and Research Institute, Wuhan 430064, China
*
Author to whom correspondence should be addressed.
Academic Editor: Fazal M. Mahomed
Received: 5 January 2017 / Revised: 6 March 2017 / Accepted: 6 March 2017 / Published: 15 March 2017
View Full-Text   |   Download PDF [2425 KB, uploaded 15 March 2017]   |  

Abstract

The development of computational acoustics allows the simulation of sound generation and propagation in a complex environment. In particular, meshfree methods are widely used to solve acoustics problems through arbitrarily distributed field points and approximation smoothness flexibility. As a Lagrangian meshfree method, the smoothed particle hydrodynamics (SPH) method reduces the difficulty in solving problems with deformable boundaries, complex topologies, or multiphase medium. The traditional SPH method has been applied in acoustic simulation. This study presents the corrective smoothed particle method (CSPM), which is a combination of the SPH kernel estimate and Taylor series expansion. The CSPM is introduced as a Lagrangian approach to improve the accuracy when solving acoustic wave equations in the time domain. Moreover, a boundary treatment technique based on the hybrid meshfree and finite difference time domain (FDTD) method is proposed, to represent different acoustic boundaries with particles. To model sound propagation in pipes with different boundaries, soft, rigid, and absorbing boundary conditions are built with this technique. Numerical results show that the CSPM algorithm is consistent and demonstrates convergence with exact solutions. The main computational parameters are discussed, and different boundary conditions are validated as being effective for benchmark problems in computational acoustics. View Full-Text
Keywords: computational acoustics; meshfree method; Lagrangian approach; smoothed particle hydrodynamics; corrective smoothed particle method; boundary conditions; numerical method computational acoustics; meshfree method; Lagrangian approach; smoothed particle hydrodynamics; corrective smoothed particle method; boundary conditions; numerical method
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Zhang, Y.O.; Li, X.; Zhang, T. Modeling Sound Propagation Using the Corrective Smoothed Particle Method with an Acoustic Boundary Treatment Technique. Math. Comput. Appl. 2017, 22, 26.

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