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Optimized finite-difference (DRP) schemes perform poorly for decaying or growing oscillations
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Brambley, Edward J. (2016) Optimized finite-difference (DRP) schemes perform poorly for decaying or growing oscillations. Journal of Computational Physics, 324 . pp. 258-274. doi:10.1016/j.jcp.2016.08.003
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Official URL: http://dx.doi.org/10.1016/j.jcp.2016.08.003
Abstract
Computational aeroacoustics often use finite difference schemes optimized to require relatively few points per wavelength; such optimized schemes are often called Dispersion Relation Preserving (DRP). Similar techniques are also used outside aeroacoustics. Here the question is posed: what is the equivalent of points per wavelength for growing or decaying waves, and how well are such waves resolved numerically? Such non-constant-amplitude waves are common in aeroacoustics, such as the exponential decay caused by acoustic linings, the O(1/r) decay of an expanding spherical wave, and the decay of high-azimuthal-order modes in the radial direction towards the centre of a cylindrical duct. It is shown that optimized spatial derivatives perform poorly for waves that are not of constant amplitude, under performing maximal-order schemes. An equivalent criterion to points per wavelength is proposed for non-constant-amplitude oscillations, reducing to the standard definition for constant-amplitude oscillations and valid even for pure growth or decay with no oscillation. Using this definition, coherent statements about points per wavelength necessary for a given accuracy can be made for maximal-order schemes applied to non-constant-amplitude oscillations. These features are illustrated through a numerical example of a one-dimensional wave propagating through a damping region.
| Item Type: | Journal Article | |||||||||
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| Subjects: | Q Science > QA Mathematics Q Science > QC Physics T Technology > TL Motor vehicles. Aeronautics. Astronautics |
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| Divisions: | Faculty of Science > Mathematics Faculty of Science > WMG (Formerly the Warwick Manufacturing Group) |
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| Library of Congress Subject Headings (LCSH): | Finite differences, Aerodynamic noise, Aerodynamic noise--Mathematics, Dispersion relations, Sound-waves--Damping , Sound-waves | |||||||||
| Journal or Publication Title: | Journal of Computational Physics | |||||||||
| Publisher: | Academic Press Inc. Elsevier Science | |||||||||
| ISSN: | 0021-9991 | |||||||||
| Official Date: | 1 November 2016 | |||||||||
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| Volume: | 324 | |||||||||
| Page Range: | pp. 258-274 | |||||||||
| DOI: | 10.1016/j.jcp.2016.08.003 | |||||||||
| Status: | Peer Reviewed | |||||||||
| Publication Status: | Published | |||||||||
| Access rights to Published version: | Restricted or Subscription Access | |||||||||
| RIOXX Funder/Project Grant: |
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