Universität zu Köln

Kopriva, David A., Nordstrom, Jan ORCID: 0000-0002-7972-6183 and Gassner, Gregor J. ORCID: 0000-0002-1752-1158 (2021). On the Theoretical Foundation of Overset Grid Methods for Hyperbolic Problems: Well-Posedness and Conservation. Technical Report.

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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 ususally 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.

Item Type:	Monograph (Technical Report)
Creators:	Creators Email ORCID ORCID Put Code Kopriva, David A. kopriva@math.fsu.edu UNSPECIFIED UNSPECIFIED Nordstrom, Jan jan.nordstrom@liu.se https://orcid.org/0000-0002-7972-6183 UNSPECIFIED Gassner, Gregor J. ggassner@uni-koeln.de https://orcid.org/0000-0002-1752-1158 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-535520
Series Name at the University of Cologne:	Technical report series. Center for Data and Simulation Science
Volume:	2021-09
Date:	6 October 2021
Language:	English
Faculty:	Central Institutions / Interdisciplinary Research Centers
Divisions:	Center for Data and Simulation Science
Subjects:	Natural sciences and mathematics Mathematics Technology (Applied sciences)
Uncontrolled Keywords:	Keywords Language Overset Grids English Chimera Method English Well-Posedness English Stability English Conservation English Penalty Methods English
Refereed:	No
URI:	http://kups.ub.uni-koeln.de/id/eprint/53552