Discontinuous subgrid formulations for transport problems |
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| Authors: | Natalia CB Arruda Regina C Almeida Eduardo G Dutra do Carmo |
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| Affiliation: | 1. The Computational Modeling Program, Laboratório Nacional de Computação Científica – LNCC/MCT, Av. Getúlio Vargas, 333 Petrópolis, RJ 25651-075, Brazil;2. Department of Computational Mechanics, Laboratório Nacional de Computação Científica – LNCC/MCT, Av. Getúlio Vargas, 333 Petrópolis, RJ 25651-075, Brazil;3. Department of Nuclear Engineering, COPPE/UFRJ – Universidade Federal do Rio de Janeiro, P.B. 68503, Rio de Janeiro, RJ, Brazil;1. Universitat Politècnica de Catalunya, Jordi Girona 1-3, Edifici C1, E-08034 Barcelona, Spain;2. Centre Internacional de Mètodes Numèrics en Enginyeria, Parc Mediterrani de la Tecnologia, Esteve Terrades 5, E-08860 Castelldefels, Spain;1. Collaborative Innovation Centre of Mathematics, School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China;2. Department of Applied Mathematics, Chung Yuan Christian University, Jhongli City, Taoyuan County 32023, Taiwan;3. Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543, Singapore;4. Department of Mathematics, National Central University, Jhongli City, Taoyuan County 32001, Taiwan;1. Department of Civil and Environmental Engineering, University of Tennessee, Knoxville, 318 John D. Tickle Engineering Building, Knoxville, TN 37996-2313, United States;2. Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, 3129E Newmark Civil Engineering Laboratory, MC-250, Urbana, IL 61801-2352, United States;1. Faculty of Engineering, Tel Aviv University, 69978 Ramat Aviv, Israel;2. Afeka, Tel Aviv Academic College of Engineering, Israel |
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| Abstract: | In this paper we develop two discontinuous Galerkin formulations within the framework of the two-scale subgrid method for solving advection–diffusion-reaction equations. We reformulate, using broken spaces, the nonlinear subgrid scale (NSGS) finite element model in which a nonlinear eddy viscosity term is introduced only to the subgrid scales of a finite element mesh. Here, two new subgrid formulations are built by introducing subgrid stabilized terms either at the element level or on the edges by means of the residual of the approximated resolved scale solution inside each element and the jump of the subgrid solution across interelement edges. The amount of subgrid viscosity is scaled by the resolved scale solution at the element level, yielding a self adaptive method so that no additional stabilization parameter is required. Numerical experiments are conducted in order to demonstrate the behavior of the proposed methodology in comparison with some discontinuous Galerkin methods. |
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