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Analysis of high‐order finite elements for convected wave propagation
Author(s) -
Bériot Hadrien,
Gabard Gwénaël,
PerreyDebain Emmanuel
Publication year - 2013
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.4559
Subject(s) - finite element method , mathematics , dispersion (optics) , mean flow , mathematical analysis , wave propagation , aliasing , exponential function , flow (mathematics) , helmholtz equation , convergence (economics) , finite difference , acoustics , helmholtz free energy , mechanics , physics , boundary value problem , computer science , geometry , engineering , structural engineering , turbulence , optics , telecommunications , quantum mechanics , undersampling , economics , economic growth
SUMMARY In this paper, we examine the performance of high‐order finite element methods (FEM) for aeroacoustic propagation, based on the convected Helmholtz equation. A methodology is presented to measure the dispersion and amplitude errors of the p ‐FEM, including non‐interpolating shape functions, such as ‘bubble’ shape functions. A series of simple test cases are also presented to support the results of the dispersion analysis. The main conclusion is that the properties of p ‐FEM that make its strength for standard acoustics (e.g., exponential p ‐convergence, low dispersion error) remain present for flow acoustics as well. However, the flow has a noticeable effect on the accuracy of the numerical solution, even when the change in wavelength due to the mean flow is accounted for, and an approximation of the dispersion error is proposed to describe the influence of the mean flow. Also discussed is the so‐called aliasing effect, which can reduce the accuracy of the solution in the case of downstream propagation. This can be avoided by an appropriate choice of mesh resolution. Copyright © 2013 John Wiley & Sons, Ltd.