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. J. Sci. Comput., 81 (2). S. 820 - 845. NEW YORK: SPRINGER/PLENUM PUBLISHERS. ISSN 1573-7691

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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. (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.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Bohm, Marvin UNSPECIFIED UNSPECIFIED UNSPECIFIED Schermeng, Sven UNSPECIFIED UNSPECIFIED UNSPECIFIED Winters, Andrew R. UNSPECIFIED UNSPECIFIED UNSPECIFIED Gassner, Gregor J. UNSPECIFIED UNSPECIFIED UNSPECIFIED Jacobs, Gustaaf B. UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-129796
DOI:	10.1007/s10915-019-01036-8
Journal or Publication Title:	J. Sci. Comput.
Volume:	81
Number:	2
Page Range:	S. 820 - 845
Date:	2019
Publisher:	SPRINGER/PLENUM PUBLISHERS
Place of Publication:	NEW YORK
ISSN:	1573-7691
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language 2-DIMENSIONAL RIEMANN PROBLEMS; GAS-DYNAMICS; ACCURACY; SCHEMES; RESOLUTION; REGULARIZATION Multiple languages Mathematics, Applied Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/12979