Print Email Facebook Twitter A discontinuous Galerkin residual-based variational multiscale method for modeling subgrid-scale behavior of the viscous Burgers equation Title A discontinuous Galerkin residual-based variational multiscale method for modeling subgrid-scale behavior of the viscous Burgers equation Author Stoter, Stein K.F. (University of Minnesota Twin Cities) Turteltaub, S.R. (TU Delft Aerospace Structures & Computational Mechanics) Hulshoff, S.J. (TU Delft Aerodynamics) Schillinger, Dominik (University of Minnesota Twin Cities) Date 2018 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. Subject Burgers turbulenceDiscontinuous Galerkin methodsResidual-based multiscale modelingVariational multiscale method To reference this document use: http://resolver.tudelft.nl/uuid:d4706f01-2f6d-45c5-8f6d-9d35a1f1a22b DOI https://doi.org/10.1002/fld.4662 Embargo date 2019-02-01 ISSN 0271-2091 Source International Journal for Numerical Methods in Fluids, 88 (5), 217-238 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. Part of collection Institutional Repository Document type journal article Rights © 2018 Stein K.F. Stoter, S.R. Turteltaub, S.J. Hulshoff, Dominik Schillinger Files PDF IJNMF2017_Stoter_et_al_po ... review.pdf 1.81 MB PDF Stoter_et_al_2018_Interna ... Fluids.pdf 2.05 MB Close viewer /islandora/object/uuid:d4706f01-2f6d-45c5-8f6d-9d35a1f1a22b/datastream/OBJ1/view