Positivity for Convective Semi-discretizations

Handle URI:
http://hdl.handle.net/10754/623303
Title:
Positivity for Convective Semi-discretizations
Authors:
Fekete, Imre; Ketcheson, David I. ( 0000-0002-1212-126X ) ; Loczi, Lajos ( 0000-0002-7999-5658 )
Abstract:
We propose a technique for investigating stability properties like positivity and forward invariance of an interval for method-of-lines discretizations, and apply the technique to study positivity preservation for a class of TVD semi-discretizations of 1D scalar hyperbolic conservation laws. This technique is a generalization of the approach suggested in Khalsaraei (J Comput Appl Math 235(1): 137–143, 2010). We give more relaxed conditions on the time-step for positivity preservation for slope-limited semi-discretizations integrated in time with explicit Runge–Kutta methods. We show that the step-size restrictions derived are sharp in a certain sense, and that many higher-order explicit Runge–Kutta methods, including the classical 4th-order method and all non-confluent methods with a negative Butcher coefficient, cannot generally maintain positivity for these semi-discretizations under any positive step size. We also apply the proposed technique to centered finite difference discretizations of scalar hyperbolic and parabolic problems.
KAUST Department:
Division of Computer, Electrical, and Mathematical Sciences & Engineering, King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia
Citation:
Fekete I, Ketcheson DI, Lóczi L (2017) Positivity for Convective Semi-discretizations. Journal of Scientific Computing. Available: http://dx.doi.org/10.1007/s10915-017-0432-9.
Publisher:
Springer Nature
Journal:
Journal of Scientific Computing
Issue Date:
19-Apr-2017
DOI:
10.1007/s10915-017-0432-9
ARXIV:
arXiv:1610.00228
Type:
Article
ISSN:
0885-7474; 1573-7691
Sponsors:
This work was supported by the King Abdullah University of Science and Technology (KAUST), 4700 Thuwal, 23955-6900, Saudi Arabia. The first author was also supported by the Tempus Public Foundation. The third author was also supported by the Department of Numerical Analysis, Eötvös Loránd University, and the Department of Differential Equations, Budapest University of Technology and Economics, Hungary.
Additional Links:
http://link.springer.com/article/10.1007/s10915-017-0432-9
Appears in Collections:
Articles

Full metadata record

DC FieldValue Language
dc.contributor.authorFekete, Imreen
dc.contributor.authorKetcheson, David I.en
dc.contributor.authorLoczi, Lajosen
dc.date.accessioned2017-05-01T06:05:15Z-
dc.date.available2017-05-01T06:05:15Z-
dc.date.issued2017-04-19en
dc.identifier.citationFekete I, Ketcheson DI, Lóczi L (2017) Positivity for Convective Semi-discretizations. Journal of Scientific Computing. Available: http://dx.doi.org/10.1007/s10915-017-0432-9.en
dc.identifier.issn0885-7474en
dc.identifier.issn1573-7691en
dc.identifier.doi10.1007/s10915-017-0432-9en
dc.identifier.urihttp://hdl.handle.net/10754/623303-
dc.description.abstractWe propose a technique for investigating stability properties like positivity and forward invariance of an interval for method-of-lines discretizations, and apply the technique to study positivity preservation for a class of TVD semi-discretizations of 1D scalar hyperbolic conservation laws. This technique is a generalization of the approach suggested in Khalsaraei (J Comput Appl Math 235(1): 137–143, 2010). We give more relaxed conditions on the time-step for positivity preservation for slope-limited semi-discretizations integrated in time with explicit Runge–Kutta methods. We show that the step-size restrictions derived are sharp in a certain sense, and that many higher-order explicit Runge–Kutta methods, including the classical 4th-order method and all non-confluent methods with a negative Butcher coefficient, cannot generally maintain positivity for these semi-discretizations under any positive step size. We also apply the proposed technique to centered finite difference discretizations of scalar hyperbolic and parabolic problems.en
dc.description.sponsorshipThis work was supported by the King Abdullah University of Science and Technology (KAUST), 4700 Thuwal, 23955-6900, Saudi Arabia. The first author was also supported by the Tempus Public Foundation. The third author was also supported by the Department of Numerical Analysis, Eötvös Loránd University, and the Department of Differential Equations, Budapest University of Technology and Economics, Hungary.en
dc.publisherSpringer Natureen
dc.relation.urlhttp://link.springer.com/article/10.1007/s10915-017-0432-9en
dc.rightsThe final publication is available at Springer via http://dx.doi.org/10.1007/s10915-017-0432-9en
dc.subjectPositivityen
dc.subjectRunge–Kuttaen
dc.subjectTotal variation diminishingen
dc.subjectStrong stability preservingen
dc.titlePositivity for Convective Semi-discretizationsen
dc.typeArticleen
dc.contributor.departmentDivision of Computer, Electrical, and Mathematical Sciences & Engineering, King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabiaen
dc.identifier.journalJournal of Scientific Computingen
dc.eprint.versionPost-printen
dc.identifier.arxividarXiv:1610.00228en
kaust.authorFekete, Imreen
kaust.authorKetcheson, David I.en
kaust.authorLoczi, Lajosen
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