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Multi-element SIAC Filter for Shock Capturing Applied to High-Order Discontinuous Galerkin Spectral Element Methods
University of Cologne, Cologne, Germany.
University of Cologne, Cologne, Germany.
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-5902-1522
University of Cologne, Cologne, Germany.
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2019 (English)In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, ISSN 0885-7474, Vol. 81, no 2, p. 820-844Article in journal (Refereed) Published
Abstract [en]

We build a multi-element variant of the smoothness increasing accuracy conserving (SIAC) shock capturing technique proposed for single element spectral methods by Wissink et al. (J Sci Comput 77:579–596, 2018). In particular, the baseline scheme of our method is the nodal discontinuous Galerkin spectral element method (DGSEM) for approximating the solution of systems of conservation laws. It is well known that high-order methods generate spurious oscillations near discontinuities which can develop in the solution for nonlinear problems, even when the initial data is smooth. We propose a novel multi-element SIAC filtering technique applied to the DGSEM as a shock capturing method. We design the SIAC filtering such that the numerical scheme remains high-order accurate and that the shock capturing is applied adaptively throughout the domain. The shock capturing method is derived for general systems of conservation laws. We apply the novel SIAC filter to the two-dimensional Euler and ideal magnetohydrodynamics equations to several standard test problems with a variety of boundary conditions.

Place, publisher, year, edition, pages
Springer-Verlag New York, 2019. Vol. 81, no 2, p. 820-844
Keywords [en]
Discontinuous Galerkin, Nonlinear hyperbolic conservation laws, SIAC filtering, Shock capturing
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-160123DOI: 10.1007/s10915-019-01036-8ISI: 000491440200008OAI: oai:DiVA.org:liu-160123DiVA, id: diva2:1349094
Funder
EU, European Research Council, 714487
Note

Funding agencies:  Linkoping University; European Research Council (ERC) under the European Unions Eights Framework Program Horizon 2020 with the research project Extreme, ERCEuropean Research Council (ERC) [714487]; NSF-DMSNational Science Foundation (NSF) [1115705]

Available from: 2019-09-06 Created: 2019-09-06 Last updated: 2019-11-05Bibliographically approved

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Winters, Andrew Ross

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  • apa
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