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Meccanica

, Volume 53, Issue 6, pp 1241–1269 | Cite as

Variational multiscale modeling with discontinuous subscales: analysis and application to scalar transport

  • Christopher Coley
  • John A. Evans
Novel Computational Approaches to Old and New Problems in Mechanics

Abstract

We examine a variational multiscale method in which the unresolved fine-scales are approximated element-wise using a discontinuous Galerkin method. We establish stability and convergence results for the methodology as applied to the scalar transport problem, and we prove that the method exhibits optimal convergence rates in the SUPG-norm and is robust with respect to the Péclet number if the discontinuous subscale approximation space is sufficiently rich. We apply the method to isogeometric NURBS discretizations of steady and unsteady transport problems, and the corresponding numerical results demonstrate that the method is stable and accurate in the advective limit even when low-order discontinuous subscale approximations are employed.

Keywords

Variational multiscale analysis Residual-free bubbles Discontinuous Galerkin methods Scalar transport 

Notes

Acknowledgements

The authors would like to acknowledge early conversations with Thomas J.R. Hughes and J. Austin Cottrell which motivated the subject of this paper. The authors would also like to thank the anonymous referees whose comments improved the quality of this paper.

Funding

This material is based upon work supported by the Air Force Office of Scientific Research under Grant No. FA9550-14-1-0113.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

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Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.Ann and H.J. Smead Department of Aerospace Engineering SciencesUniversity of Colorado BoulderBoulderUSA

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