Dealiasing techniques for high-order spectral element methods on regular and irregular grids
File(s)
Published version
Author(s)
Mengaldo, G
De Grazia, D
Moxey, D
Vincent, P
Sherwin, S
Type
Journal Article
Abstract
High-order methods are becoming increasingly attractive in both academia and industry, especially in the context of computational fluid dynamics. However, before they can be more widely adopted, issues such as lack of robustness in terms of numerical stability need to be addressed, particularly when treating industrial-type problems where challenging geometries and a wide range of physical scales, typically due to high Reynolds numbers, need to be taken into account. One source of instability is aliasing effects which arise from the nonlinearity of the underlying problem. In this work we detail two dealiasing strategies based on the concept of consistent integration. The first uses a localised approach, which is useful when the nonlinearities only arise in parts of the problem. The second is based on the more traditional approach of using a higher quadrature. The main goal of both dealiasing techniques is to improve the robustness of high order spectral element methods, thereby reducing aliasing-driven instabilities. We demonstrate how these two strategies can be effectively applied to both continuous and discontinuous discretisations, where, in the latter, both volumetric and interface approximations must be considered. We show the key features of each dealiasing technique applied to the scalar conservation law with numerical examples and we highlight the main differences in terms of implementation between continuous and discontinuous spatial discretisations.
Date Issued
2015-10-15
Date Acceptance
2015-06-28
Citation
Journal of Computational Physics, 2015, 299 (1), pp.56-81
ISSN
0021-9991
Publisher
Elsevier
Start Page
56
End Page
81
Journal / Book Title
Journal of Computational Physics
Volume
299
Issue
1
Copyright Statement
© 2015 The Authors. Published by Elsevier Inc. This
is an open access article under the CC BY-NC-ND
license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
is an open access article under the CC BY-NC-ND
license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Sponsor
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (E
Identifier
https://www.sciencedirect.com/science/article/pii/S0021999115004301
Grant Number
EP/K027379/1
EP/I037946/1
Subjects
Science & Technology
Technology
Physical Sciences
Computer Science, Interdisciplinary Applications
Physics, Mathematical
Computer Science
Physics
Dealiasing
Spectral/hp methods
Continuous Galerkin
Discontinuous Galerkin
Flux reconstruction
VANISHING VISCOSITY METHOD
VARIATIONAL MULTISCALE METHOD
DISCONTINUOUS GALERKIN METHOD
LARGE-EDDY SIMULATIONS
STABILIZATION
ALGORITHMS
ADVECTION
ERRORS
FLOWS
01 Mathematical Sciences
02 Physical Sciences
09 Engineering
Applied Mathematics
Publication Status
Published
Date Publish Online
2015-07-07