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One-dimensional shock-capturing for high-order discontinuous Galerkin methods

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Casoni Rero, Eva
Peraire Guitart, Jaume
Huerta, AntonioMés informacióMés informacióMés informació
Document typeArticle
Defense date2012-02
Rights accessOpen Access
Attribution-NonCommercial-NoDerivs 3.0 Spain
Except where otherwise noted, content on this work is licensed under a Creative Commons license : Attribution-NonCommercial-NoDerivs 3.0 Spain
Abstract
Discontinuous Galerkin methods have emerged in recent years as an alternative for nonlinear conservation equations. In particular, their inherent structure (a numerical flux based on a suitable approximate Riemann solver introduces some stabilization) suggests that they are specially adapted to capture shocks. However, numerical fluxes are not sufficient to stabilize the solution in the presence of shocks. Thus, slope limiter methods, which are extensions of finite volume methods, have been proposed. These techniques require, in practice, mesh adaption to localize the shock structure. This is is more obvious for large elements typical of high-order approximations. Here, a new approach based on the introduction of artificial diffusion into the original equations is presented. The order is not systematically decreased to one in the presence of the shock, large high-order elements can be used, and several linear and nonlinear tests demonstrate the efficiency of the proposed methodology.
CitationCasoni, E., Peraire, J., Huerta, A. One-dimensional shock-capturing for high-order discontinuous Galerkin methods. "International journal for numerical methods in fluids", Febrer 2012, vol. 71, núm. 6, p. 737-755. 
URIhttp://hdl.handle.net/2117/79962
DOI10.1002/fld.3682
ISSN0271-2091
Publisher versionhttp://cataleg.upc.edu/record=b1208224~S1*cat
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