Technical Brief

An Efficient Algorithm of Wiener–Hopf Method With Graphics Processing Unit for Duct Acoustics

[+] Author and Article Information
Hanbo Jiang

College of Engineering,
Peking University,
Beijing 100871, China
e-mail: jianghb@pku.edu.cn

Alex Siu Hong Lau

Mechanical and Aerospace Engineering,
Hong Kong University of Science and Technology,
Kowloon 100871, Hong Kong, China
e-mail: alexshlau@ust.hk

Xun Huang

Department of Mechanical and Aerospace Engineering,
The Hong Kong University of Science and Technology,
Kowloon 100871, Hong Kong, China;
Department of Aeronautics and Astronautics,
College of Engineering,
Peking University,
Beijing 100871, China
e-mails: huangxun@ust.hk; huangxun@pku.edu.cn

1Corresponding author.

Contributed by the Noise Control and Acoustics Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received January 11, 2017; final manuscript received March 29, 2017; published online July 13, 2017. Assoc. Editor: Ronald N. Miles.

J. Vib. Acoust 139(5), 054501 (Jul 13, 2017) (8 pages) Paper No: VIB-17-1012; doi: 10.1115/1.4036471 History: Received January 11, 2017; Revised March 29, 2017

Acoustic liner optimization calls for very efficient simulation methods. A highly efficient and straightforward algorithm is proposed here for the Wiener–Hopf solver, which also takes advantage of the parallel processing capability of the emerging graphics processing unit (GPU) technology. The proposed algorithm adopts a simple concept that re-arranges the formulations of the Wiener–Hopf solver to appropriate matrix forms. This concept was often overlooked but is surprisingly succinct, which leads to a stunningly efficient computational performance. By examining the computational performance of two representative setups (lined duct and duct radiations), the current study shows the superior performance of the proposed algorithm, particularly with GPU. The much improved computational efficiency further suggests the potential of the proposed algorithm and the use of GPU for practical low-noise aircraft engine design and optimization.

Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.


Tester, B. , 1973, “ Some Aspects of Sound Attenuation in Lined Ducts Containing Inviscid Mean Flows With Boundary Layers,” J. Sound Vib., 28(2), pp. 217–245. [CrossRef]
Oliveira, J. , and Gil, P. , 2014, “ Sound Propagation in Acoustically Lined Elliptical Ducts,” J. Sound Vib., 333(16), pp. 3743–3758. [CrossRef]
Bianchi, S. , Corsini, A. , Rispoli, F. , and Sheard, A. G. , 2011, “ Far-Field Radiation of Tip Aerodynamic Sound Sources in Axial Fans Fitted With Passive Noise Control Features,” ASME J. Vib. Acoust., 133(5), p. 051001. [CrossRef]
Bogey, C. , Bailly, C. , and Juvé, D. , 2002, “ Computation of Flow Noise Using Source Terms in Linearized Euler's Equations,” AIAA J., 40(2), pp. 235–243. [CrossRef]
Agarwal, A. , Morris, P. J. , and Mani, R. , 2004, “ Calculation of Sound Propagation in Nonuniform Flows: Suppression of Instability Waves,” AIAA J., 42(1), pp. 80–88. [CrossRef]
Richter, C. , Thiele, F. , Li, X. , and Zhuang, M. , 2007, “ Comparison of Time-Domain Impedance Boundary Conditions for Lined Duct Flows,” AIAA J., 45(6), pp. 1333–1345. [CrossRef]
Huang, X. , Chen, X. , Ma, Z. , and Zhang, X. , 2008, “ Efficient Computation of Spinning Modal Radiation Through an Engine Bypass Duct,” AIAA J., 46(6), pp. 1413–1423. [CrossRef]
Casalino, D. , and Genito, M. , 2008, “ Turbofan Aft Noise Predictions Based on Lilley's Wave Model,” AIAA J., 46(1), pp. 84–93. [CrossRef]
Chen, X. , Huang, X. , and Zhang, X. , 2009, “ Sound Radiation From a Bypass Duct With Bifurcations,” AIAA J., 47(2), pp. 429–436. [CrossRef]
Zhang, X. , 2012, “ Aircraft Noise and Its Nearfield Propagation Computations,” Acta Mech. Sin., 28(4), pp. 960–977. [CrossRef]
Jiang, H. B. , and Huang, X. , 2017, “ Efficient Impedance Eductions for Liner Tests in Grazing Flow Incidence Tube,” ASME J. Vib. Acoust., 139(3), p. 031002. [CrossRef]
Noble, B. , 1958, Methods Beased on the Wiener–Hopf Technique for the Solution of Partial Differential Equations, Pergamon Press, Oxford, UK, pp. 46–47.
Munt, R. M. , 1977, “ The Interaction of Sound With a Subsonic Jet Issuing From a Semi-Infinite Cylindrical Pipe,” J. Fluid Mech., 83(4), pp. 609–640. [CrossRef]
Rienstra, S. W. , 1984, “ Acoustic Radiation From a Semi-Infinite Annular Duct in a Uniform Subsonic Mean Flow,” J. Sound Vib., 94(2), pp. 267–288. [CrossRef]
Rienstra, S. W. , 2007, “ Acoustic Scattering at a Hard-Soft Lining Transition in a Flow Duct,” J. Eng. Math., 59(4), pp. 451–475. [CrossRef]
Gabard, G. , and Astley, R. , 2006, “ Theoretical Model for Sound Radiation From Annular Jet Pipes: Far- and Near-Field Solutions,” J. Fluid Mech., 549, pp. 315–341. [CrossRef]
Liu, X. , Jiang, H. B. , Huang, X. , and Chen, S. , 2016, “ Theoretical Model of Scattering From Flow Ducts With Semi-Infinite Axial Liner Splices,” J. Fluid Mech., 786, pp. 62–83. [CrossRef]
Brandvik, T. , and Pullan, G. , 2008, “ Acceleration of a 3D Euler Solver Using Commodity Graphics Hardware,” AIAA Paper No. 2008-607.
Elsen, E. , LeGresley, P. , and Darve, E. , 2008, “ Large Calculation of the Flow Over a Hypersonic Vehicle Using a GPU,” J. Comput. Phys., 227(24), pp. 10148–10161. [CrossRef]
Rossinelli, D. , Bergdorf, M. , Cottet, G.-H. , and Koumoutsakos, P. , 2010, “ GPU Accelerated Simulations of Bluff Body Flows Using Vortex Particle Methods,” J. Comput. Phys., 229(9), pp. 3316–3333. [CrossRef]
Weigel, M. , 2012, “ Performance Potential for Simulating Spin Models on GPU,” J. Comput. Phys., 231(8), pp. 3064–3082. [CrossRef]
Salvadore, F. , Bernardini, M. , and Botti, M. , 2013, “ GPU Accelerated Flow Solver for Direct Numerical Simulation of Turbulent Flows,” J. Comput. Phys., 235, pp. 129–142. [CrossRef]
Tutkun, B. , and Edis, F. , 2012, “ A GPU Application for High-Order Compact Finite Difference Scheme,” Comput. Fluids, 55, pp. 29–35. [CrossRef]
Komatitsch, D. , Erlebacher, G. , Göddeke, D. , and Michéa, D. , 2010, “ High-Order Finite-Element Seismic Wave Propagation Modeling With MPI on a Large GPU Cluster,” J. Comput. Phys., 229(20), pp. 7692–7714. [CrossRef]
Yiu, B. , Tsang, I. , and Yu, A. , 2011, “ GPU-Based Beamformer: Fast Realization of Plane Wave Compounding and Synthetic Aperture Imaging,” IEEE Trans. Ultrason., Ferroelectr., Freq. Control, 58(8), pp. 1698–1705. [CrossRef]
Miao, S. , Zhang, X. , Parchment, O. , and Chen, X. , 2015, “ A Fast GPU Based Bidiagonal Solver for Computational Aeroacoustics,” Comput. Methods Appl. Mech. Eng., 286, pp. 22–39. [CrossRef]
Song, W. , and Keane, A. , 2007, “ Surrogate-Based Aerodynamic Shape Optimization of a Civil Aircraft Engine Nacelle,” AIAA J., 45(10), pp. 2565–2574. [CrossRef]
Press, W. H. , 1996, Numerical Recipes in Fortran 77, Cambridge Press, Cambridge, UK, pp. 123–158.
Garland, M. , Grand, S. , Nickolls, J. , Anderson, J. , Hardwick, J. , Morton, S. , Phillips, E. , Zhang, Y. , and Volkov, V. , 2008, “ Parallel Computing Experiences With CUDA,” IEEE Micro Mag., 28(4), pp. 13–27. [CrossRef]


Grahic Jump Location
Fig. 1

A sketch of the axial-symmetrical, semi-infinitely lined duct problem [15], where ξl denotes the presumably straight and infinitely thin vortex sheet that develops from the lining surface. For clarity, ξl is shown here in an exaggerated way. In addition, the notations ξl+ and ξl− represent the upper and lower sides of the vortex sheet, respectively; M0 is the Mach number of the presumably uniform flow accommodated in the duct; and M1=0 is the Mach number of the boundary flow local to the lining surface. Other parameters are given in the main text.

Grahic Jump Location
Fig. 2

(a) Schematic of the two complex half-planes R± and the overlapped strip when M = 0.3, as duplicated from Fig. 2 of our previous work [17]. (b) The path of integration (solid line) for Eq. (16) will be slightly deformed to around all possible acoustic zeros (“°”) and poles (x).

Grahic Jump Location
Fig. 3

(a) The programming model of CUDA and (b) the programming flowchart for our work

Grahic Jump Location
Fig. 4

The way matrix A in Eq. (22) is mapped to stream processors and simultaneously calculated on GPU

Grahic Jump Location
Fig. 5

Computational costs for (a) the kernel factorization K+(μ) and (b) the calculation of the entire sound pressure field. Here, we consider both the proposed new algorithm and the old version algorithm, and compare the related costs on the CPU and GPU platforms, respectively. The horizontal axis is the matrix size. The vertical axes are the corresponding computational time in second: the left vertical axis of each panel is for the current proposed algorithm, while the right vertical axis displays the much longer computational time by using the old version algorithm with CPU. Other parameters of the test case are given in the main text.

Grahic Jump Location
Fig. 6

Near-field sound pressure contours of a semi-infinitely lined cylindrical duct case, where the spinning mode is (m,n)=(4,1), the normalized acoustic impedance is Z=1+1i at ω = 10 and M0=0.5. (a) An instantaneous sound pressure and (b) the sound pressure level.

Grahic Jump Location
Fig. 7

Sketch of the model setup for the classical test case from Munt [13]. M0 is the Mach number of the ambient flow, and Mj is the Mach number of the jet flow.

Grahic Jump Location
Fig. 8

The near-field sound pressure contours. The Munt case [13]: ω = 10, Mode(4,1), and M0=0.5. (a) An instantaneous sound pressure field and (b) the sound pressure level.



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In