Universität zu Köln

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:	Monograph (Technical Report)
Creators:	Creators Email ORCID ORCID Put Code Bohm, Marvin UNSPECIFIED UNSPECIFIED UNSPECIFIED Schermeng, Sven UNSPECIFIED UNSPECIFIED UNSPECIFIED Winters, Andrew R. andrew.ross.winters@liu.se UNSPECIFIED UNSPECIFIED Gassner, Gregor J. ggassner@math.uni-koeln.de UNSPECIFIED UNSPECIFIED Jacobs, Gustaaf B. gjacobs@mail.sdsu.edu UNSPECIFIED UNSPECIFIED
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
Date:	12 July 2019
Language:	English
Faculty:	Central Institutions / Interdisciplinary Research Centers
Divisions:	Weitere Institute, Arbeits- und Forschungsgruppen > Center for Data and Simulation Science (CDS)
Subjects:	Natural sciences and mathematics Mathematics Technology (Applied sciences)
Uncontrolled Keywords:	Keywords Language Discontinuous Galerkin English nonlinear hyperbolic conservation laws English SIAC filtering English Shock capturing English
URI:	http://kups.ub.uni-koeln.de/id/eprint/9782