Spatial eigensolution analysis of energy-stable flux reconstruction schemes and influence of the numerical flux on accuracy and robustness
File(s)
Published version
Author(s)
Mengaldo, Gianmarco
De Grazia, Daniele
Moura, RC
Sherwin, Spencer
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.
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.
Date Issued
2018-01-06
Date Acceptance
2017-12-13
Citation
Journal of Computational Physics, 2018, 358, pp.1-20
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/)
CC BY license (http://creativecommons.org/licenses/by/4.0/)
License URL
Sponsor
Engineering & Physical Science Research Council (E
Royal Academy Of Engineering
Engineering & Physical Science Research Council (EPSRC)
Grant Number
EP/I037946/1
AEDZ_P40009
EP/L000407/1
Subjects
01 Mathematical Sciences
02 Physical Sciences
09 Engineering
Applied Mathematics
Publication Status
Published online
Date Publish Online
2018-01-06