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

Mengaldo, Gianmarco and De Grazia, Daniele and Moura, Rodrigo C. and Sherwin, Spencer J. (2018) Spatial eigensolution analysis of energy-stable flux reconstruction schemes and influence of the numerical flux on accuracy and robustness. Journal of Computational Physics, 358 . pp. 1-20. ISSN 0021-9991. http://resolver.caltech.edu/CaltechAUTHORS:20180109-073456986

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Abstract

This study focuses on the dispersion and diffusion characteristics of high-order energy-stable flux reconstruction (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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/j.jcp.2017.12.019DOIArticle
https://www.sciencedirect.com/science/article/pii/S0021999117309051PublisherArticle
Additional Information:© 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/). Received 27 July 2017, Revised 3 November 2017, Accepted 13 December 2017, Available online 6 January 2018. We would like to gratefully acknowledge the computing facilities provided by the Imperial College High Performance Computing Service without which this work would have not been possible. RCM would like to acknowledge support from the Brazilian Science without Borders scheme. SJS acknowledges support as Royal Academy of Engineering Research Chair under grant 10145/86 and support under EPSRC grant EP/L000407/1.
Funders:
Funding AgencyGrant Number
Brazilian Science without BordersUNSPECIFIED
Royal Academy of Engineering Research Chair10145/86
Engineering and Physical Sciences Research Council (EPSRC)EP/L000407/1
Subject Keywords:Eigensolution analysis; Spectral element methods; Flux Reconstruction; Implicit LES; Under-resolved DNS
Record Number:CaltechAUTHORS:20180109-073456986
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20180109-073456986
Official Citation:Gianmarco Mengaldo, Daniele De Grazia, Rodrigo C. Moura, Spencer J. Sherwin, Spatial eigensolution analysis of energy-stable flux reconstruction schemes and influence of the numerical flux on accuracy and robustness, Journal of Computational Physics, Volume 358, 2018, Pages 1-20, ISSN 0021-9991, https://doi.org/10.1016/j.jcp.2017.12.019. (http://www.sciencedirect.com/science/article/pii/S0021999117309051)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:84179
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:09 Jan 2018 15:49
Last Modified:02 Mar 2018 19:34

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