Print Email Facebook Twitter Residual-based variational multiscale modeling in a discontinuous Galerkin framework Title Residual-based variational multiscale modeling in a discontinuous Galerkin framework 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 2018-01-01 Abstract We develop the general form of the variational multiscale method in a discontinuous Galerkin framework. Our method is based on the decomposition of the true solution into discontinuous coarse-scale and discontinuous fine-scale parts. The obtained coarse-scale weak formulation includes two types of fine-scale contributions. The first type corresponds to a fine-scale volumetric term, which we formulate in terms of a residual-based model that also takes into account fine-scale effects at element interfaces. The second type consists of independent fine-scale terms at element interfaces, which we formulate in terms of a new fine-scale "interface model." We demonstrate for the one-dimensional Poisson problem that existing discontinuous Galerkin formulations, such as the interior penalty method, can be rederived by choosing particular fine-scale interface models. The multiscale formulation thus opens the door for a new perspective on discontinuous Galerkin methods and their numerical properties. This is demonstrated for the one-dimensional advection-diffusion problem, where we show that upwind numerical fluxes can be interpreted as an ad hoc remedy for missing volumetric fine-scale terms. Subject Multiscale discontinuous Galerkin methodsResidual-based multiscale modelingUpwindingVariational multiscale method To reference this document use: http://resolver.tudelft.nl/uuid:b4fccf77-cd61-4434-9959-67670a39df38 DOI https://doi.org/10.1137/17M1147044 Embargo date 2019-04-01 ISSN 1540-3459 Source Multiscale Modeling and Simulation, 16 (3), 1333-1364 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 17m1147044.pdf 1.57 MB Close viewer /islandora/object/uuid:b4fccf77-cd61-4434-9959-67670a39df38/datastream/OBJ/view