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On the Spurious Mode Generation Induced by Spectral-Like Optimized Interpolation Schemes Used in Computational Acoustics

Part of: Approximations and expansions Basic methods in fluid mechanics Numerical approximation and computational geometry

Published online by Cambridge University Press:  21 July 2016

Guilherme Cunha  and
Stéphane Redonnet
Guilherme Cunha
Affiliation:
Department of Numerical Fluid Mechanics, Onera – French Aerospace Lab, F-92322 Châtillon, France
Stéphane Redonnet*
Affiliation:
Department of Aeroacoustics, Onera – French Aerospace Lab, F-92322 Châtillon, France
*
*Corresponding author. Email address:[email protected] (S. Redonnet)
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Abstract

The present work constitutes a fraction of a more extensive study that is devoted to numerical methods in acoustics. More precisely, we address here the interpolation process, which is more and more frequently used in Computational Acoustics–whether it is for enabling multi-stage hybrid calculations, or for easing the proper handling of complex configurations via advanced techniques such as Chimera grids or Immersed Boundary Conditions. In that regard, we focus on high-order interpolation schemes, so as to analyze their intrinsic features and to assess their effective accuracy. Taking advantage of specific insights that had been previously achieved by the present authors regarding standard high-order interpolation schemes (of centered nature), we here focus on their so-called spectral-like optimized counterparts (of both centered and noncentered nature). The latter spectral-like optimized schemes are analyzed thoroughly thanks to dedicated theoretical developments, which allow highlighting better what their strengths and weaknesses are. Among others, the various ways such interpolation schemes can degrade acoustic signals they are applied to are carefully investigated from a theoretical point-of-view. Besides that, specific criteria that could help in optimizing interpolation schemes better are provided, along with generic rules about how to minimize the signal degradation induced by existing interpolation schemes, in practice.

Keywords

Noncentered interpolationcentered interpolationhigh-orderspectral-like optimizationspurious modes generationcomputational acoustics

MSC classification

Secondary: 65D05: Interpolation 76M25: Other numerical methods 41A05: Interpolation
Type
Research Article
Information
Communications in Computational Physics , Volume 20 , Issue 2 , August 2016 , pp. 325 - 352
Copyright
Copyright © Global-Science Press 2016 

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References

[1] Tam, C. K. W., Computational aeroacoustics: An overview of computational challenges and applications, Journal of Computational Fluid Dynamics 18 (6) (2004) 247–567.Google Scholar
[2] Sherer, S. E., Scott, J. N., High-order compact finite-difference methods on general overset grids, Journal of Computational Physics 210 (2) (2005) 459–496.CrossRefGoogle Scholar
[3] Redonnet, S., Cunha, G., An advanced hybrid method for the acoustic prediction, Advances in Engineering Software 88 (2015) 30–52.CrossRefGoogle Scholar
[4] Redonnet, S., Simulation de la propagation acoustique en presence d’ecoulements quelconques et de structures solides, par resolution numerique des equations d’Euler, Ph.D. thesis, Universite Bordeaux I, Bordeaux (Oct. 2001).Google Scholar
[5] Redonnet, S., Lockard, D., Khorrami, D., Choudhari, M., The non reflective interface: an innovative forcing technique for computational acoustics hybrid methods, International Journal for Numerical Methods in Fluids 81 (1) (2016) 22–44.CrossRefGoogle Scholar
[6] Manoha, E., Herrero, C., Sagaut, P., Redonnet, S., Numerical prediction of airfoil aerodynamic noise, AIAA Paper 2002-2573.CrossRefGoogle Scholar
[7] Terracol, M., Manoha, E., Herrero, C., Labourasse, E., Redonnet, S., Sagaut, P., Hybrid methods for airframe noise numerical prediction, Theoretical and Computational Fluid Dynamics 19 (3) (2005) 197–227.CrossRefGoogle Scholar
[8] Desquesnes, G., Terracol, M., Manoha, E., Sagaut, P., On the use of high order overlapping grid method for coupling in CFD/CAA, Journal of Computational Physics 220 (1) (2006) 355–382.CrossRefGoogle Scholar
[9] Tam, C. K. W., Kurbatskii, K. A., Multi-size-mesh multi-time-step dispersion-relation-preserving scheme for multiple-scales aeroacoustics problems, International Journal of Computational Fluid Dynamics 17 (2) (2003) 119–132.CrossRefGoogle Scholar
[10] Tam, C. K. W., Kurbatskii, K. A., An optimized extrapolation and interpolation method for computational aeroacoustics, AIAA Paper 2001-0282.CrossRefGoogle Scholar
[11] Pellers, N., Duc, A. L., Tremblay, F., Manhart, M., High-order stable interpolations for immersed boundary methods, International Journal for Numerical Methods in Fluids 52 (11) (2006) 1175–1193.CrossRefGoogle Scholar
[12] Desvigne, D., Mardsen, O., Bogey, C., Bailly, C., Development of noncentered wavenumber-based optimized interpolation schemes with amplification control for overlapping grids, SIAM Journal of Scientific Computing 32 (4) (2010) 2074–2098.CrossRefGoogle Scholar
[13] Schafer, R. W., Rabiner, L. R., A digital signal processing approach to interpolation, Proceedings of the IEEE 61 (6) (1973) 692–702.CrossRefGoogle Scholar
[14] Cunha, G., Redonnet, S., On the signal degradation induced by the interpolation and the sampling rate reduction in aeroacoustics hybrid methods, International Journal for Numerical Methods in Fluids (DOI: 10.1002/fld.3693) 71 (7) (2013) 910–929.CrossRefGoogle Scholar
[15] Boyd, J. P., Chebyshev and Fourier Spectral Methods, Springer-Verlag, 1989.CrossRefGoogle Scholar
[16] Schmid, P., An Introduction to Computational Fluid Dynamics, John Wiley and Sons Inc., 2007.Google Scholar
[17] Cunha, G., Redonnet, S., Development of optimized interpolation schemes with spurious modes minimization, International Journal for Numerical Methods in Fluids 80 (2016) 140–158.CrossRefGoogle Scholar
[18] Kurbatskii, K. A., Tam, C. K. W., Cartesian boundary treatment of curvedwalls for high-order computational aeroacoustics schemes, AIAA Journal 35 (1) (1997) 133–140.CrossRefGoogle Scholar