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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

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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
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
T Technology > TL Motor vehicles. Aeronautics. Astronautics
Divisions: Faculty of Science > Mathematics
Faculty of Science > WMG (Formerly the Warwick Manufacturing Group)
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
Dates:
DateEvent
1 November 2016Published
11 August 2016Available
3 August 2016Accepted
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:
Project/Grant IDRIOXX Funder NameFunder ID
UF100844Royal Societyhttp://dx.doi.org/10.13039/501100000288
UNSPECIFIEDGonville and Caius College, University of Cambridgehttp://dx.doi.org/10.13039/501100000622
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