Skip to main content
Log in

Recent advances of computational aeroacoustics

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

Computational aeroacoustics (CAA) is an interdiscipline of aeroacoustics and computational fluid dynamics (CFD) for the investigation of sound generation and propagation from various aeroacoustics problems. In this review, the foundation and research scope of CAA are introduced firstly. A review of the early advances and applications of CAA is then briefly surveyed, focusing on two key issues, namely, high order finite difference scheme and non-reflecting boundary condition. Furthermore, the advances of CAA during the past five years are highlighted. Finally, the future prospective of CAA is briefly discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Lighthill, M. J. On sound generated aerodynamically: I. general theory. Proc. R. Soc. Lond. A., 211(1107), 564–587 (1952)

    Article  MathSciNet  MATH  Google Scholar 

  2. Lighthill, M. J. On sound generated aerodynamically: II. turbulence as a source of sound. Proc. R. Soc. Lond. A., 211(1148), 1–32 (1954)

    Google Scholar 

  3. Ffowcs Williams, J. E. and Hawkings, D. L. Sound generated by turbulence and surfaces in arbitrary motion. Phil. Trans. R. Soc. Lond. A., 264(1151), 321–342 (1969)

    Article  MATH  Google Scholar 

  4. Tam, C. K. W. Computational aeroacoustics: issues and method. AIAA J., 33(10), 1788–1796 (1995)

    Article  MATH  Google Scholar 

  5. Tam, C. K. W. Advances in numerical boundary conditions for computational aeroacoustics. J. Comput. Acoust., 6(4), 377–402 (1998)

    Article  Google Scholar 

  6. Tam, C. K. W. Computational aeroacoustics: an overview of computational challenges and applications. Int. J. Comput. Fluid Dyn., 18(6), 547–567 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  7. Tam, C. K. W. Computational Aeroacoustics, A Wave Number Approach, Cambridge University Press, New York, 263–265 (2012)

    Book  MATH  Google Scholar 

  8. Lele, S. K. Computational aeroacoustics: a review. 35th Aerospace Sciences Meeting and Exhibit, 97-0018, American Institute of Aeronautics and Astronautics, Reno (1997)

    Google Scholar 

  9. Li, X. D., Jiang, M., Gao, J. H., Lin, D. K., Liu, L., and Li, X. Y. Progress and prospective of computational aeroacoustics (in Chinese). Sci. China Phys. Mech., 44(3), 234–248 (2014)

    Google Scholar 

  10. Lele, S. K. Compact finite difference scheme with spectral-like resolution. J. Comput. Phys., 103(1), 16–42 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  11. Tam, C. K. W. and Webb, J. C. Dispersion-relation-preserving finite difference scheme for computational acoustics. J. Comput. Phys., 107(2), 262–281 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  12. Kim, J. W. and Lee, D. J. Optimized compact finite difference schemes with maximum resolution. AIAA J., 34(5), 887–893 (1996)

    Article  MATH  Google Scholar 

  13. Zhong, X. L. High-order finite-difference schemes for numerical simulation of hypersonic boundarylayer transition. J. Comput. Phys., 144(2), 662–709 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  14. Zhuang, M. and Chen, R. Optimized upwind dispersion-relation-preserving finite difference scheme for computational aeroacoustics. AIAA J., 35(11), 2146–2148 (1998)

    Article  Google Scholar 

  15. Gaitonde, D. and Shang, J. S. Optimized compact-difference-based finite-volume schemes for linear wave phenomena. J. Comput. Phys., 138(2), 617–643 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  16. Lee, C. and Seo, Y. A new compact spectral scheme for turbulence simulation. J. Comput. Phys., 183(2), 438–469 (2002)

    Article  MATH  Google Scholar 

  17. Bogey, C. and Bailly, C. A family of low dispersive and low dissipative explicit schemes for flow and noise computations. J. Comput. Phys., 194(1), 194–214 (2004)

    Article  MATH  Google Scholar 

  18. Berland, J., Bogey, C., and Marsden, O. High-order low dispersive and low dissipative explicit schemes for multiple-scale and boundary problems. J. Comput. Phys., 224(2), 637–662 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  19. Hu, F. Q., Hussaini, M. Y., and Manthey, J. L. Low-dissipation and low-dispersion Runge-Kutta schemes for computational acoustics. J. Comput. Phys., 124(1), 177–191 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  20. Stanescu, D. and Habashi, W. G. 2N-storage low-dissipation and low-dispersion Runge-Kutta schemes for computational aeroacoustics. J. Comput. Phys., 143(2), 674–681 (1998)

    Article  MATH  Google Scholar 

  21. Bayliss, A. and Turkel, E. Radiation boundary conditions for wave-like equations. Commun. Pur. Appl. Math., 33(6), 707–725 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  22. Bayliss, A. and Turkel, E. Far filed boundary conditions for compressible flows. J. Comput. Phys., 48(2), 182–199 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  23. Hagstrom, T. and Hariharan, S. I. Accurate boundary conditions for exterior problems in gas dynamics. Math. Comput., 51, 581–597 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  24. Tam, C. K. W. and Dong, Z. Radiation and outflow boundary conditions for direct computation of acoustic and flow disturbances in a non-uniform mean flow. J. Comput. Acoust., 4(2), 175–201 (1996)

    Article  Google Scholar 

  25. Giles, M. B. Nonreflecting boundary conditions for Euler equation calculations. AIAA J., 28(12), 2050–2058 (1990)

    Article  Google Scholar 

  26. Thompson, K.W. Time dependent boundary conditions for hypersonic systems. J. Comput. Phys., 68(1), 1–24 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  27. Thompson, K. W. Time dependent boundary conditions for hypersonic systems, II. J. Comput. Phys., 89(8), 439–461 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  28. Poinsot, T. J. and Lele, S. K. Boundary conditions for direct simulations of compressible viscous flows. J. Comput. Phys., 101(7), 104–129 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  29. Berenger, J. P. A perfectly matched layer for the absorption of electromagnetic waves. J. Comput. Phys., 114(2), 185–200 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  30. Hu, F. Q. On absorbing boundary conditions for linearized Euler equations by a perfectly matched layer. J. Comput. Phys., 129(1), 201–219 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  31. Abarbanel, S., Gottlieb, D., and Hesthaven, J. S. Well-posed perfectly matched layers for advective acoustics. J. Comput. Phys., 154(2), 266–283 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  32. Appelö, D., Hagstrom, T., and Kreiss, G. Perfectly matched layers for hyperbolic systems: general formulation, well-posedness and stability. SIAM J. Appl. Maths., 67(1), 1–23 (2006)

    Article  MATH  Google Scholar 

  33. Hu, F. Q. A stable perfectly matched layer for linearized Euler equations in unsplit physical variables. J. Comput. Phys., 173(2), 455–480 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  34. Hu, F. Q. A perfectly matched layer absorbing boundary condition for linearized Euler equations with a non-uniform mean-flow. J. Comput. Phys., 208(2), 469–492 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  35. Özyörük, Y., Alpman, E., Ahuja, V., and Long, L. N. Frequency-domain prediction of turbofan noise radiation. J. Sound Vib., 270(4-5), 933–950 (2004)

    Article  Google Scholar 

  36. Li, X. D., Schemel, C., Michel, U., and Thiele, F. H. Azimuthal sound mode propagation in axisymmetric flow ducts. AIAA J., 42(10), 2019–2027 (2004)

    Article  Google Scholar 

  37. Li, X. D., Richter, C., and Thiele, F. Time-domain impedance boundary conditions for surfaces with subsonic mean flows. J. Acoust. Soc. Am., 119(5), 2665–2676 (2006)

    Article  Google Scholar 

  38. Shen, H. and Tam, C. K. W. Three-dimensional numerical simulation of the jet screech phenomenon. AIAA J., 40(1), 33–41 (2002)

    Article  Google Scholar 

  39. Li, X. D. and Gao, J. H. Numerical simulation of the generation mechanism of axisymmetric supersonic jet screech tones. Phys. Fluids, 17(8), 085105 (2005)

    Google Scholar 

  40. Bogey, C. and Bailly, C. Large eddy simulations of transitional round jets: influence of the Reynolds number on flow development and energy dissipation. Phys. Fluids, 18(6), 065101 (2006)

    Google Scholar 

  41. Bogey, C. and Bailly, C. Large eddy simulations of round free jets using explicit filtering with/without dynamic Smagorinsky model. Int. J. Heat Fluid Flow, 27(4), 603–610 (2006)

    Article  Google Scholar 

  42. Li, X. D. and Gao, J. H. Numerical simulation of the three dimensional screech phenomenon from a circular jet. Phys. Fluids, 20(3), 035101 (2008)

    Google Scholar 

  43. Tam, C. K. W. and Kurbatskii, K. A. Micro fluid dynamics and acoustics of resonant liners. AIAA J., 38(8), 1331–1339 (2000)

    Article  Google Scholar 

  44. Tam, C. K. W. and Ju, H. Numerical simulation of the generation of airfoil tones at a moderate Reynolds number. 12th AIAA/CEAS Aeroacoustics Conference (27th AIAA Aeroacoustics Conference), 2006-2502, American Institute of Aeronautics and Astronautics, Cambridge (2006)

    Google Scholar 

  45. Liu, Y., Vinokur, M., and Wang, Z. J. Spectral difference method for unstructured grids I: basic formulation. J. Comput. Phys., 216(2), 780–801 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  46. Wang, Z. J., Liu, Y., May, G., and Jameson, A. Spectral difference method for unstructured grids II: extension to the Euler equations. J. Sci. Comput., 32(1), 45–71 (2006)

    Article  MathSciNet  Google Scholar 

  47. Sun, Y., Wang, Z. J., and Liu, Y. High-order multidomain spectral difference method for the Navier-Stokes equations on unstructured hexahedral grids. Commun. Comput. Phys., 2(2), 310–333 (2007)

    MathSciNet  MATH  Google Scholar 

  48. Gao, J. H., Yang, Z. G., and Li, X. D. An optimized spectral difference method for CAA problems. J. Comput. Phys., 231(14), 4848–4866 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  49. Gao, J. H. A block interface flux reconstruction method for numerical simulation with high order finite difference scheme. J. Comput. Phys., 241(15), 1–17 (2013)

    Article  Google Scholar 

  50. Fernando, A. M. and Hu, F. Q. A finite difference scheme based on the discontinuous Galerkin method applied to wave propagation. 14th AIAA/CEAS Aeroacoustics Conference (29th AIAA Aeroacoustics Conference), 2008-2874, American Institute of Aeronautics and Astronautics, Vancouver (2008)

    Google Scholar 

  51. Tam, C. K. W. and Kurbastkii, K. A. Multi-size-mesh multi-time-step dispersion relation preserving scheme for multi-scales aeroacoustics problems. Int. J. Comput. Fluid Dyn, 17(2), 119–132 (2003)

    Article  MATH  Google Scholar 

  52. Shen, H. and Tam, C. K. W. Three-dimensional numerical simulation of the jet screech phenomenon. AIAA J., 40(1), 33–41 (2002)

    Article  Google Scholar 

  53. Garrec, T. L., Gloerfelt, X., and Corre, C. Multi-size-mesh multi-time-step algorithm for noise computation around an airfoil in curvilinear meshes. 13th AIAA/CEAS Aeroacoustics Conference (28th AIAA Aeroacoustics Conference), 2007-3504, American Institute of Aeronautics and Astronautics, Rome (2007)

    Google Scholar 

  54. Liu, L., Li, X. D., and Hu, F. Q. Non-uniform time-step explicit Runge-Kutta discontinuous Galerkin method for computational aeroacoustics. J. Comput. Phys., 229(19), 6874–6897 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  55. Liu, L., Li, X. D., and Hu, F. Q. Nonuniform-time-step explicit Rung-Kutta scheme for highorder finite difference method. 16th AIAA/CEAS Aeroacoustics Conference, 2010-3934, American Institute of Aeronautics and Astronautics, Stockholm (2010)

    Google Scholar 

  56. Bauer, M., Dierke, J., and Ewert, R. On the performance of airframe noise prediction on unstructured grids. 8th AIAA/CEAS Aeroacoustics Conference (33rd AIAA Aeroacoustics Conference), 2012-2148, American Institute of Aeronautics and Astronautics, Colorado (2012)

    Google Scholar 

  57. Lin, D. K., Jiang, M., and Li, X. D. A multi-time-step strategy based on an optimized time interpolation scheme for overset grids. J. Comput. Acoust., 18(2), 131–148 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  58. Gao, J. H. and Li, X. D. Detached eddy simulation of flow over NACA0012 airfoil at high angle of attack with spectral difference method. 52nd Aerospace Sciences Meeting, 2014-0425, American Institute of Aeronautics and Astronautics, Maryland (2014)

    Google Scholar 

  59. Allampalli, V. Fourth Order Multi-Time-Stepping Adam-Bashforth (MTSAB) Scheme for NASA Glenn Research Center’s Broadband Aeroacoustic Stator Simulation (BASS) Code, Ph. D. dissertation, The University of Toledo, 3–5 (2010)

    Google Scholar 

  60. Hu, F. Q., Li, X. D., and Lin, D. K. Absorbing boundary conditions for nonlinear Euler and Navier-Stokes equations based on the perfectly matched layer technique. J. Comput. Phys., 227(9), 4398–4424 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  61. Lin, D. K., Li, X. D., and Hu, F. Q. Absorbing boundary condition for nonlinear Euler equations in primitive variables based on the perfectly matched layer technique. Comput. Fluids, 40(1), 333–337 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  62. Parrish, S. A. and Hu, F. Q. PML absorbing boundary conditions for the linearized and nonlinear Euler equations in the case of oblique mean flow. Int. J. Numer. Meth. Fluids, 60(5), 565–589 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  63. Tam, C. K. W. and Auriault, L. Time domain impedance boundary for computational aeroacoustics. AIAA J., 34(5), 917–923 (1996)

    Article  MATH  Google Scholar 

  64. Özyörük, Y., Long, Y. L., and Jones, M. G. Time-domain numerical simulation of a flow-impedance tube. J. Comput. Phys., 146(1), 29–57 (1998)

    Article  MATH  Google Scholar 

  65. Rienstra, S. W. Impedance models in time domain, including the extended Helmholtz resonator model. 12th AIAA/CEAS Aeroacoustics Conference (27th AIAA Aeroacoustics Conference), 2006-2686, American Institute of Aeronautics and Astronautics, Cambridge (2006)

    Google Scholar 

  66. Reymen, Y., Baelmans, M., and Desmet, W. Efficient implementation of Tam and Auriault’s time-domain impedance boundary condition. AIAA J., 46(9), 2368–2376 (2008)

    Article  Google Scholar 

  67. Li, X. Y., Li, X. D., and Tam, C. K.W. An improved multi-pole broadband time domain impedance boundary condition. AIAA J., 50(4), 980–984 (2012)

    Article  Google Scholar 

  68. Xu, J., Li, X. D., and Guo, Y. P. Nonlinear absorbing characteristic of micro resonator under high sound pressure level. 20th AIAA/CEAS Aeroacoustics Conference, 2014-3353, American Institute of Aeronautics and Astronautics, Atlanta (2014)

    Google Scholar 

  69. Wang, M., Freund, J. B., and Lele, S. K. Computational prediction of flow-generated sound. Annu. Rev. Fluid Mech., 38, 483–512 (2006)

    Article  MathSciNet  Google Scholar 

  70. He, G. W., Rubinstein, R., and Wang, L. P. Effects of subgrid-scale modeling on time correlations in large eddy simulation. Phys. Fluids, 14(7), 2186–2193 (2002)

    Article  Google Scholar 

  71. He, G. W., Wang, M., and Lele, S. K. On the computation of space-time correlations by large-eddy simulation. Phys. Fluids, 16(11), 3859–3867 (2004)

    Article  Google Scholar 

  72. LaBryer, A., Attar, P. J., and Vedula, P. Optimal spatiotemporal reduced order modeling, part I: proposed framework. Comput. Mech., 52(2), 417–431 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  73. Seid, K. H., Gilka, G., Leung, R. C. K., and Thiele, F. A Comparison study of reduced order models for aeroacoustics applications. 18th AIAA/CEAS Aeroacoustics Conference (33rd AIAA Aeroacoustics Conference), 2012-2072, American Institute of Aeronautics and Astronautics, Colorado (2012)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Xiao-dong Li.

Additional information

Project supported by the National Basic Research Program of China (No. 2012CB720202), the National Natural Science Foundation of China (No. 51476005), and the 111 Project of China (No. B07009)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, Xd., Jiang, M., Gao, Jh. et al. Recent advances of computational aeroacoustics. Appl. Math. Mech.-Engl. Ed. 36, 131–140 (2015). https://doi.org/10.1007/s10483-015-1899-9

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-015-1899-9

Key words

Chinese Library Classification

2010 Mathematics Subject Classification

Navigation