Universität zu Köln

Markert, Johannes, Gassner, Gregor J. ORCID: 0000-0002-1752-1158 and Walch, Stefanie ORCID: 0000-0001-6941-7638 (2020). A Sub-Element Adaptive Shock Capturing Approach for Discontinuous Galerkin Methods. Technical Report.

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Abstract

In this paper, a new strategy for a sub-element based shock capturing for discontinuous Galerkin (DG) approximations is presented. The idea is to interpret a DG element as a collection of data and construct a hierarchy of low to high order discretizations on this set of data, including a first order finite volume scheme up to the full order DG scheme. The different DG discretizations are then blended according to sub-element troubled cell indicators, resulting in a final discretization that adaptively blends from low to high order within a single DG element. The goal is to retain as much high order accuracy as possible, even in simulations with very strong shocks, as e.g. presented in the Sedov test. The framework retains the locality of the standard DG scheme and is hence well suited for a combination with adaptive mesh refinement and parallel computing. The numerical tests demonstrate the sub-element adaptive behavior of the new shock capturing approach and its high accuracy.

Item Type:	Monograph (Technical Report)
Creators:	Creators Email ORCID ORCID Put Code Markert, Johannes jmarkert@math.uni-koeln.de UNSPECIFIED UNSPECIFIED Gassner, Gregor J. ggassner@math.uni-koeln.de https://orcid.org/0000-0002-1752-1158 UNSPECIFIED Walch, Stefanie UNSPECIFIED https://orcid.org/0000-0001-6941-7638 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-250548
Series Name at the University of Cologne:	Technical report series. Center for Data and Simulation Science
Volume:	2020,10
Date:	6 November 2020
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 shock capturing English compressible Euler equations English sub-element resolution English
Refereed:	No
URI:	http://kups.ub.uni-koeln.de/id/eprint/25054