A discontinuous Galerkin residual-based variational multiscale method for modeling subgrid-scale behavior of the viscous Burgers equation

Stein K.F. Stoter*, Sergio R. Turteltaub, Steven J. Hulshoff, Dominik Schillinger

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

3 Citations (Scopus)
75 Downloads (Pure)

Abstract

We initiate the study of the discontinuous Galerkin residual-based variational multiscale (DG-RVMS) method for incorporating subgrid-scale behavior into the finite element solution of hyperbolic problems. We use the one-dimensional viscous Burgers equation as a model problem, as its energy dissipation mechanism is analogous to that of turbulent flows. We first develop the DG-RVMS formulation for a general class of nonlinear hyperbolic problems with a diffusion term, based on the decomposition of the true solution into discontinuous coarse-scale and fine-scale components. In contrast to existing continuous variational multiscale methods, the DG-RVMS formulation leads to additional fine-scale element interface terms. For the Burgers equation, we devise suitable models for all fine-scale terms that do not use ad hoc devices such as eddy viscosities but instead directly follow from the nature of the fine-scale solution. In comparison to single-scale discontinuous Galerkin methods, the resulting DG-RVMS formulation significantly reduces the energy error of the Burgers solution, demonstrating its ability to incorporate subgrid-scale behavior in the discrete coarse-scale system.
Original languageEnglish
Pages (from-to)217-238
Number of pages22
JournalInternational Journal for Numerical Methods in Fluids
Volume88
Issue number5
DOIs
Publication statusPublished - 2018

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Keywords

  • Burgers turbulence
  • Discontinuous Galerkin methods
  • Residual-based multiscale modeling
  • Variational multiscale method

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