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On the theoretical ...
On the theoretical foundation of overset grid methods for hyperbolic problems : Well-posedness and conservation
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- Kopriva, David A. (författare)
- The Florida State University, USA; San Diego State University, USA
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- Nordström, Jan, 1953- (författare)
- Linköpings universitet,Tillämpad matematik,Tekniska fakulteten,University of Johannesburg, South Africa
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- Gassner, Gregor J. (författare)
- University of Cologne, Germany
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(creator_code:org_t)
- ACADEMIC PRESS INC ELSEVIER SCIENCE, 2022
- 2022
- Engelska.
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Ingår i: Journal of Computational Physics. - : ACADEMIC PRESS INC ELSEVIER SCIENCE. - 0021-9991 .- 1090-2716. ; 448
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Abstract
Ämnesord
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- 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.
Ämnesord
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Nyckelord
- Overset grids
- Chimera method
- Well-posedness
- Stability
- Conservation
- Penalty methods
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
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