Variational multiscale modeling with discontinuous subscales: analysis and application to scalar transport
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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.
KeywordsVariational multiscale analysis Residual-free bubbles Discontinuous Galerkin methods Scalar transport
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.
This material is based upon work supported by the Air Force Office of Scientific Research under Grant No. FA9550-14-1-0113.
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Conflict of interest
The authors declare that they have no conflict of interest.
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