Dealiasing techniques for high-order spectral element methods on regular and irregular grids
J. Comput. Phys., vol. 299, pp. 56–81 (2015)
@article{mengaldo-2015,
title = {{Dealiasing techniques for high-order spectral element methods on regular and irregular grids}},
author = {Mengaldo, G. and de Grazia, D. and Moxey, D. and Vincent, P. E. and Sherwin, S. J.},
journal = jcp,
year = {2015},
volume = {299},
pages = {56--81},
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 of which uses a localised approach which is useful when the nonlinearities only arise in parts of the problem and the second a 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 implementation between continuous and discontinuous spatial discretisations.},
doi = {10.1016/j.jcp.2015.06.032},
url = {http://www.sciencedirect.com/science/article/pii/S0021999115004301}
}
High-order methods can lose numerical stability on industrial problems, and one source of that is the aliasing introduced by nonlinear terms. This paper sets out two dealiasing strategies based on consistent integration: a localised one for when the nonlinearity arises only in part of the problem, and the more traditional route of a higher quadrature. Both are applied to continuous and discontinuous discretisations, where the discontinuous case also requires the interface terms to be treated.
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 of which uses a localised approach which is useful when the nonlinearities only arise in parts of the problem and the second a 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 implementation between continuous and discontinuous spatial discretisations.