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

Variational multiscale modeling with discontinuous subscales: analysis and application to scalar... 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Meccanica Springer Journals

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

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Publisher
Springer Netherlands
Copyright
Copyright © 2017 by Springer Science+Business Media B.V.
Subject
Physics; Classical Mechanics; Civil Engineering; Automotive Engineering; Mechanical Engineering
ISSN
0025-6455
eISSN
1572-9648
D.O.I.
10.1007/s11012-017-0786-y
Publisher site
See Article on Publisher Site

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.

Journal

MeccanicaSpringer Journals

Published: Nov 8, 2017

References

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