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Spatial eigensolution analysis of energy-stable flux reconstruction schemes and influence of the numerical flux on accuracy and robustness

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Title: Spatial eigensolution analysis of energy-stable flux reconstruction schemes and influence of the numerical flux on accuracy and robustness
Authors: Mengaldo, G
De Grazia, D
Moura, RC
Sherwin, S
Item Type: Journal Article
Abstract: This study focusses on the dispersion and diffusion characteristics of high-order energy-stable flux recon- struction (ESFR) schemes via the spatial eigensolution analysis framework proposed in [1]. The analysis is performed for five ESFR schemes, where the parameter ‘ c ’ dictating the properties of the specific scheme recovered is chosen such that it spans the entire class of ESFR methods, also referred to as VCJH schemes, proposed in [ 2 ]. In particular, we used five values of ‘ c ’, two that correspond to its lower and upper bounds and the others that identify three schemes that are linked to common high-order methods, namely the ESFR recovering two versions of discontinuous Galerkin methods and one recovering the spectral difference scheme. The performance of each scheme is assessed when using different numerical intercell fluxes (e.g. different levels of upwinding), ranging from “under-” to “over-upwinding”. In contrast to the more common temporal analysis, the spatial eigensolution analysis framework adopted here allows one to grasp crucial insights into the diffusion and dispersion properties of FR schemes for problems involving non-periodic boundary conditions, typically found in open-flow problems, including turbulence, unsteady aerodynamics and aeroacoustics.
Issue Date: 6-Jan-2018
Date of Acceptance: 13-Dec-2017
URI: http://hdl.handle.net/10044/1/55723
DOI: https://dx.doi.org/10.1016/j.jcp.2017.12.019
ISSN: 0021-9991
Publisher: Elsevier
Start Page: 1
End Page: 20
Journal / Book Title: Journal of Computational Physics
Volume: 358
Copyright Statement: © 2017 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/)
Sponsor/Funder: Engineering & Physical Science Research Council (E
Royal Academy Of Engineering
Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/I037946/1
AEDZ_P40009
EP/L000407/1
Keywords: 01 Mathematical Sciences
02 Physical Sciences
09 Engineering
Applied Mathematics
Publication Status: Published online
Appears in Collections:Faculty of Engineering
Aeronautics



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