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Research Papers: Fluid-Structure Interaction

A Cell-Based Smoothed Radial Point Interpolation—Perfectly Matched Layer Method For Two-Dimensional Acoustic Radiation Problems

[+] Author and Article Information
Lingyun Yao

College of Engineering and Technology,
Southwest University,
Chongqing 400715, China
e-mail: 19831022y@163.com

Yunwu Li, Li Li

College of Engineering and Technology,
Southwest University,
Chongqing 400715, China

1Corresponding author.

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received November 7, 2014; final manuscript received September 15, 2015; published online November 18, 2015. Assoc. Editor: Jong Chull Jo.

J. Pressure Vessel Technol 138(2), 021301 (Nov 18, 2015) (9 pages) Paper No: PVT-14-1182; doi: 10.1115/1.4031720 History: Received November 07, 2014; Revised September 15, 2015

We present a cell-based smoothed radial point interpolation method (CS-RPIM) model for two-dimensional acoustic radiating problem by incorporating the perfectly matched layer method (PML). In this work, the computational region, truncated by PML, is discretized into triangular background cells. Each cell is further divided into several smoothing cells, and then the cell-based gradient smoothing operation is implemented throughout the smoothing cells. The pressure field function is approximated using the RPIM shape functions. The supporting node selection for shape function construction uses the T2L-scheme associated with edges of the background cells. The cell-based gradient smoothing operation provides proper softening effect, and makes the acoustic stiffness of the CS-RPIM model much softer than that of the FEM (finite element method)/PML model, which in turn significantly reduces the numerical dispersion error. Numerical results show that, compared with FEM–PML, the CS-RPIM achieves better absorbing effect in the PML, and higher accuracy in the computational region. This enables us to conclude that the CS-RPIM model with the PML can be well applied in solving acoustic radiation problems.

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Figures

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Fig. 1

Regions of the PML model of radiation acoustic field

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Fig. 2

Subdivision of a parent cell into SC smoothing cells

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Fig. 3

Two-dimensional steady-state radiation acoustic cavity model of tube

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Fig. 4

The background cells model of two-dimensional radiation domain of tube

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Fig. 5

Real part of the pressure field (absolute value, Pa) at 40 Hz predicted with (a) FEM/PML and (b) CS-RPIM/PML

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Fig. 6

Amplitude part of the pressure field (Pa) at 40 Hz predicted with (a) FEM/PML and (b) CS-RPIM/PML

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Fig. 7

Real part of the pressure field (Pa) at 100 Hz predicted with (a) FEM/PML and (b) CS-RPIM/PML

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Fig. 8

Amplitude part of the pressure field (Pa) at 100 Hz predicted with (a) FEM/PML and (b) CS-RPIM/PML

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Fig. 15

Frequency response error curve of the pressure amplitude in field R2

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Fig. 14

Frequency response error curve of the pressure amplitude in field R1

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Fig. 13

Frequency response curve of the pressure amplitude in field R3

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Fig. 12

Frequency response curve of the pressure amplitude in field R2

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Fig. 11

Frequency response curve of the pressure amplitude in field R1

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Fig. 10

Relation between the pressure error in the computational region and thickness of PML with f = 100 Hz

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Fig. 9

Relation between the pressure error in the computational region and thickness of PML with f = 40 Hz

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