Dealiasing techniques for high-order spectral element methods on regular and irregular grids
De Grazia, D
Journal of Computational Physics
©2015 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
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.
This work was supported by the Laminar Flow Control Centre funded by Airbus/EADS and EPSRC under grant EP/I037946. We thank Dr. Colin Cotter for helpful discussions and Jean-Eloi Lombard for his assistance in the generation of results and figures for the NACA 0012 simulation. PV acknowledges the Engineering and Physical Sciences Research Council for their support via an Early Career Fellowship (EP/K027379/1). SJS additionally acknowledges Royal Academy of Engineering support under their research chair scheme. Data supporting this publication can be obtained on request from email@example.com.
This is the final version of the article. Available from Elsevier via the DOI in this record.
Vol. 299, pp. 56 - 81