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Published April 1, 2018 | Published
Journal Article Open

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

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.

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.

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August 21, 2023
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