Universität zu Köln

Friedrich, Lucas, Winters, Andrew R., Del Rey Fernandez, David C., Gassner, Gregor J., Parsani, Matteo and Carpenter, Mark H. (2019). An Entropy Stable h/p Non-Conforming Discontinuous Galerkin Method with the Summation-by-Parts Property. Technical Report.

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Abstract

This work presents an entropy stable discontinuous Galerkin (DG) spectral element approximation for systems of non-linear conservation laws with general geometric (h) and polynomial order (p) non-conforming rectangular meshes. The crux of the proofs presented is that the nodal DG method is constructed with the collocated Legendre-Gauss-Lobatto nodes. This choice ensures that the derivative/mass matrix pair is a summation-by-parts (SBP) operator such that entropy stability proofs from the continuous analysis are discretely mimicked. Special attention is given to the coupling between non- conforming elements as we demonstrate that the standard mortar approach for DG methods does not guarantee entropy stability for non-linear problems, which can lead to instabilities. As such, we describe a precise procedure and modify the mortar method to guarantee entropy stability for general non-linear hyperbolic systems on h/p non-conforming meshes. We verify the high-order accuracy and the entropy conservation/stability of fully non-conforming approximation with numerical examples.

Item Type:	Preprints, Working Papers or Reports (Technical Report)
Creators:	Creators Email ORCID ORCID Put Code Friedrich, Lucas lfriedri@math.uni-koeln.de UNSPECIFIED UNSPECIFIED Winters, Andrew R. UNSPECIFIED UNSPECIFIED UNSPECIFIED Del Rey Fernandez, David C. UNSPECIFIED UNSPECIFIED UNSPECIFIED Gassner, Gregor J. UNSPECIFIED UNSPECIFIED UNSPECIFIED Parsani, Matteo UNSPECIFIED UNSPECIFIED UNSPECIFIED Carpenter, Mark H. UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-92759
Series Name at the University of Cologne:	Technical report series. Center for Data and Simulation Science
Volume:	2019, 4
Date:	25 January 2019
Language:	English
Faculty:	Central Institutions / Interdisciplinary Research Centers
Divisions:	Weitere Institute, Arbeits- und Forschungsgruppen > Center for Data and Simulation Science (CDS)
Subjects:	Data processing Computer science Mathematics Technology (Applied sciences)
Uncontrolled Keywords:	Keywords Language Summation-by-Parts English Discontinuous Galerkin English Entropy Conservation English Entropy Stability English h/p Non-Conforming Mesh English Non-Linear Hyperbolic Conservation Laws English
URI:	http://kups.ub.uni-koeln.de/id/eprint/9275