Universität zu Köln

Friedrich, Lucas, Winters, Andrew R., Fernandez, David C. Del Rey, Gassner, Gregor J., Parsani, Matteo ORCID: 0000-0001-7300-1280 and Carpenter, Mark H. (2018). An Entropy Stable h/p Non-Conforming Discontinuous Galerkin Method with the Summation-by-Parts Property. J. Sci. Comput., 77 (2). S. 689 - 726. NEW YORK: SPRINGER/PLENUM PUBLISHERS. ISSN 1573-7691

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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:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Friedrich, Lucas UNSPECIFIED UNSPECIFIED UNSPECIFIED Winters, Andrew R. UNSPECIFIED UNSPECIFIED UNSPECIFIED Fernandez, David C. Del Rey UNSPECIFIED UNSPECIFIED UNSPECIFIED Gassner, Gregor J. UNSPECIFIED UNSPECIFIED UNSPECIFIED Parsani, Matteo UNSPECIFIED orcid.org/0000-0001-7300-1280 UNSPECIFIED Carpenter, Mark H. UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-168689
DOI:	10.1007/s10915-018-0733-7
Journal or Publication Title:	J. Sci. Comput.
Volume:	77
Number:	2
Page Range:	S. 689 - 726
Date:	2018
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 FINITE-DIFFERENCE METHODS; NAVIER-STOKES EQUATIONS; NONLINEAR CONSERVATION-LAWS; SHALLOW-WATER EQUATIONS; SCHEMES; ORDER; FORM; OPERATORS; SYSTEMS; GRIDS Multiple languages Mathematics, Applied Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/16868