Bohm, Marvin, Schermeng, Sven, Winters, Andrew R., Gassner, Gregor J. and Jacobs, Gustaaf B. (2019). Multi-element SIAC filter for shock capturing applied to high-order discontinuous Galerkin spectral element methods. Technical Report.

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Abstract

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. [37]. 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 (MHD) equations to several standard test problems with a variety of boundary conditions.

Item Type: Preprints, Working Papers or Reports (Technical Report)
Creators:
CreatorsEmailORCID
Bohm, MarvinUNSPECIFIEDUNSPECIFIED
Schermeng, SvenUNSPECIFIEDUNSPECIFIED
Winters, Andrew R.andrew.ross.winters@liu.seUNSPECIFIED
Gassner, Gregor J.ggassner@math.uni-koeln.deUNSPECIFIED
Jacobs, Gustaaf B.gjacobs@mail.sdsu.eduUNSPECIFIED
URN: urn:nbn:de:hbz:38-97823
Series Name at the University of Cologne: Technical report series. Center for Data and Simulation Science
Volume: 2019,16
Subjects: Natural sciences and mathematics
Mathematics
Technology (Applied sciences)
Uncontrolled Keywords:
KeywordsLanguage
Discontinuous GalerkinEnglish
nonlinear hyperbolic conservation lawsEnglish
SIAC filteringEnglish
Shock capturingEnglish
Faculty: Central Institutions / Interdisciplinary Research Centers
Divisions: Weitere Institute, Arbeits- und Forschungsgruppen > Center for Data and Simulation Science (CDS)
Language: English
Date: 12 July 2019
URI: http://kups.ub.uni-koeln.de/id/eprint/9782

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