Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2015, Article ID 142730, 11 pages
http://dx.doi.org/10.1155/2015/142730
Research Article

Explicit High Accuracy Maximum Resolution Dispersion Relation Preserving Schemes for Computational Aeroacoustics

1The State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China
2Yichang Testing Technique Research Institute, No. 58 Shengli 3rd Road, Yichang, Hubei 430074, China
3Reactor Engineering Testing Research Center, China Nuclear Power Technology Research Institute Co., Ltd., Shenzhen 518026, China

Received 12 February 2015; Revised 21 May 2015; Accepted 26 May 2015

Academic Editor: Vassilios C. Loukopoulos

Copyright © 2015 J. L. Wang et al. 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.

Linked References

  1. J. A. Ekaterinaris, “High-order accurate, low numerical diffusion methods for aerodynamics,” Progress in Aerospace Sciences, vol. 41, no. 3-4, pp. 192–300, 2005. View at Publisher · View at Google Scholar · View at Scopus
  2. Z. J. Wang, K. Fidkowski, R. Abgrall et al., “High-order CFD methods: current status and perspective,” International Journal for Numerical Methods in Fluids, vol. 72, no. 8, pp. 811–845, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. Y. Liu, M. Vinokur, and Z. J. Wang, “Spectral difference method for unstructured grids I: basic formulation,” Journal of Computational Physics, vol. 216, no. 2, pp. 780–801, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. B. Cockburn, “Discontinuous Galerkin methods,” ZAMM—Journal of Applied Mathematics and Mechanics, vol. 83, no. 11, pp. 731–754, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  5. G. Jiang and C. Shu, “Efficient implementation of weighted ENO schemes,” DTIC Document, 1995. View at Google Scholar
  6. H. L. Meitz and H. F. Fasel, “A compact-difference scheme for the Navier-Stokes equations in vorticity-velocity formulation,” Journal of Computational Physics, vol. 157, no. 1, pp. 371–403, 2000. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. K. Bhaganagar, D. Rempfer, and J. Lumley, “Direct numerical simulation of spatial transition to turbulence using fourth-order vertical velocity second-order vertical vorticity formulation,” Journal of Computational Physics, vol. 180, no. 1, pp. 200–228, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  8. C. K. Tam, J. C. Webb, and Z. Dong, “A study of the short wave components in computational acoustics,” Journal of Computational Acoustics, vol. 1, no. 1, pp. 1–30, 1993. View at Publisher · View at Google Scholar · View at MathSciNet
  9. J. W. Kim and P. J. Morris, “Computation of subsonic inviscid flow past a cone using high-order schemes,” AIAA Journal, vol. 40, no. 10, pp. 1961–1968, 2002. View at Publisher · View at Google Scholar · View at Scopus
  10. S. K. Lele, “Compact finite difference schemes with spectral-like resolution,” Journal of Computational Physics, vol. 103, no. 1, pp. 16–42, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  11. C. K. Tam and J. C. Webb, “Dispersion-relation-preserving finite difference schemes for computational acoustics,” Journal of Computational Physics, vol. 107, no. 2, pp. 262–281, 1993. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. J. A. Ekaterinaris, “Implicit, high-resolution, compact schemes for gas dynamics and aeroacoustics,” Journal of Computational Physics, vol. 156, no. 2, pp. 272–299, 1999. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. D. W. Zingg, “Comparison of high-accuracy finite-difference methods for linear wave propagation,” SIAM Journal on Scientific Computing, vol. 22, no. 2, pp. 476–502, 2000. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. G. Cunha and S. Redonnet, “On the effective accuracy of spectral-like optimized finite-difference schemes for computational aeroacoustics,” Journal of Computational Physics, vol. 263, pp. 222–232, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. D. P. Lockard, K. S. Brentner, and H. L. Atkins, “High-accuracy algorithms for computational aeroacoustics,” AIAA Journal, vol. 33, no. 2, pp. 246–251, 1995. View at Publisher · View at Google Scholar · View at Scopus
  16. J. W. Kim and D. J. Lee, “Optimized compact finite difference schemes with maximum resolution,” AIAA Journal, vol. 34, no. 5, pp. 887–893, 1996. View at Publisher · View at Google Scholar · View at Scopus
  17. C. Cheong and S. Lee, “Grid-optimized dispersion-relation-preserving schemes on general geometries for computational aeroacoustics,” Journal of Computational Physics, vol. 174, no. 1, pp. 248–276, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  18. Z. Liu, Q. Huang, Z. Zhao, and J. Yuan, “Optimized compact finite difference schemes with high accuracy and maximum resolution,” International Journal of Aeroacoustics, vol. 7, no. 2, pp. 123–146, 2008. View at Publisher · View at Google Scholar
  19. Z. Mei and R. Christoph, Computational Aeroacoustics and Its Applications, 2008.
  20. C. Bogey and C. Bailly, “A family of low dispersive and low dissipative explicit schemes for flow and noise computations,” Journal of Computational Physics, vol. 194, no. 1, pp. 194–214, 2004. View at Publisher · View at Google Scholar · View at Scopus
  21. M. Venutelli, “New optimized fourth-order compact finite difference schemes for wave propagation phenomena,” Applied Numerical Mathematics, vol. 87, pp. 53–73, 2015. View at Publisher · View at Google Scholar · View at MathSciNet
  22. F. Q. Hu, M. Y. Hussaini, and J. L. Manthey, “Low-dissipation and low-dispersion Runge-Kutta schemes for computational acoustics,” Journal of Computational Physics, vol. 124, no. 1, pp. 177–191, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  23. F. Q. Hu, “Development of PML absorbing boundary conditions for computational aeroacoustics: a progress review,” Computers & Fluids, vol. 37, no. 4, pp. 336–348, 2008. View at Publisher · View at Google Scholar · View at Scopus
  24. N. B. Edgar, A study of the accuracy and stability of high-order compact difference methods for computational aeroacoustics [Ph.D. thesis], University of Kansas, Lawrence, Kan, USA, 2001.
  25. S. E. Sherer, “Scattering of sound from axisymetric sources by multiple circular cylinders,” The Journal of the Acoustical Society of America, vol. 115, no. 2, pp. 488–496, 2004. View at Publisher · View at Google Scholar · View at Scopus
  26. J. H. Seo and R. Mittal, “A high-order immersed boundary method for acoustic wave scattering and low-Mach number flow-induced sound in complex geometries,” Journal of Computational Physics, vol. 230, no. 4, pp. 1000–1019, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  27. J. L. Wang, The Centered Finite Difference Scheme Coefficients in This Paper, MathWorks, Natick, Mass, USA, 2015, http://www.mathworks.com/matlabcentral/fileexchange/50934.