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5 - Numerical Methods

Published online by Cambridge University Press:  02 September 2009

Claus Wagner
Affiliation:
German Aerospace Center, Göttingen
Thomas Hüttl
Affiliation:
MTU Aero Engines GmbH, München
Pierre Sagaut
Affiliation:
Université de Paris VI (Pierre et Marie Curie)
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Summary

Spatial and temporal discretization schemes

Tim Broeckhoven, Jan Ramboer, Sergey Smirnov, and Chris Lacor

Introduction to discretization schemes

In contrast to standard computational fluid dynamics (CFD) applications, for which second-order accuracy in space is sufficient for engineering purposes, the requirements on the schemes are much more stringent in the computation of aeroacoustical applications. There are several reasons for this.

First, the amplitudes of acoustic waves are several orders of magnitude smaller than the average aerodynamic field amplitudes. In addition, the length scales of acoustic waves, typically the principal acoustic wavelengths, are some orders of magnitude larger than the dimensions of the sound-generating perturbations (vortices and turbulent eddies). Thirdly, sound generated by turbulence is broadband noise with often three orders of magnitude difference between the largest and the smallest acoustic wavelengths. Finally, acoustic waves propagate at the speed of sound (which is not necessarily comparable to the mean flow velocity) over large distances in all spatial directions, whereas aerodynamic perturbations are only convected by the mean flow. Moreover, one is usually interested in the noise level at the far field, implying that the waves have to be traced accurately over long distances.

This requires numerical methods with higher accuracy than routinely applied in CFD codes. In particular, the discretization of the convective operator (i.e., the first-order derivative) requires special attention. In this respect, the actual order of the scheme, which can be determined based on a Taylor expansion analysis, is not the primary concern.

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Publisher: Cambridge University Press
Print publication year: 2007

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  • Numerical Methods
  • Edited by Claus Wagner, German Aerospace Center, Göttingen, Thomas Hüttl, MTU Aero Engines GmbH, München, Pierre Sagaut, Université de Paris VI (Pierre et Marie Curie)
  • Book: Large-Eddy Simulation for Acoustics
  • Online publication: 02 September 2009
  • Chapter DOI: https://doi.org/10.1017/CBO9780511546143.007
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  • Numerical Methods
  • Edited by Claus Wagner, German Aerospace Center, Göttingen, Thomas Hüttl, MTU Aero Engines GmbH, München, Pierre Sagaut, Université de Paris VI (Pierre et Marie Curie)
  • Book: Large-Eddy Simulation for Acoustics
  • Online publication: 02 September 2009
  • Chapter DOI: https://doi.org/10.1017/CBO9780511546143.007
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Numerical Methods
  • Edited by Claus Wagner, German Aerospace Center, Göttingen, Thomas Hüttl, MTU Aero Engines GmbH, München, Pierre Sagaut, Université de Paris VI (Pierre et Marie Curie)
  • Book: Large-Eddy Simulation for Acoustics
  • Online publication: 02 September 2009
  • Chapter DOI: https://doi.org/10.1017/CBO9780511546143.007
Available formats
×