Universität zu Köln

Kopriva, David A., Nordstrom, Jan ORCID: 0000-0002-7972-6183 and Gassner, Gregor J. (2022). On the theoretical foundation of overset grid methods for hyperbolic problems: Well-posedness and conservation. J. Comput. Phys., 448. SAN DIEGO: ACADEMIC PRESS INC ELSEVIER SCIENCE. ISSN 1090-2716

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Abstract

We use the energy method to study the well-posedness of initial-boundary value problems approximated by overset mesh methods in one and two space dimensions for linear constant-coefficient hyperbolic systems. We show that in one space dimension, for both scalar equations and systems of equations, the problem where one domain partially oversets another is well-posed when characteristic coupling conditions are used. If a system cannot be diagonalized, as is usually the case in multiple space dimensions, then the energy method does not give proper bounds in terms of initial and boundary data. For those problems, we propose a novel penalty approach. We show, by using a global energy that accounts for the energy in the overlap region of the domains, that under well-defined conditions on the coupling matrices the penalized overset domain problems are energy bounded, conservative, well-posed and have solutions equivalent to the original single domain problem. (c) 2021 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Kopriva, David A. UNSPECIFIED UNSPECIFIED UNSPECIFIED Nordstrom, Jan UNSPECIFIED orcid.org/0000-0002-7972-6183 UNSPECIFIED Gassner, Gregor J. UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-593938
DOI:	10.1016/j.jcp.2021.110732
Journal or Publication Title:	J. Comput. Phys.
Volume:	448
Date:	2022
Publisher:	ACADEMIC PRESS INC ELSEVIER SCIENCE
Place of Publication:	SAN DIEGO
ISSN:	1090-2716
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language MULTIPLE PENALTY TERMS; NUMERICAL-METHODS; EQUATIONS Multiple languages Computer Science, Interdisciplinary Applications; Physics, Mathematical Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/59393