On the Linear Stability of the Fifth-Order WENO Discretization

Handle URI:
http://hdl.handle.net/10754/599059
Title:
On the Linear Stability of the Fifth-Order WENO Discretization
Authors:
Motamed, Mohammad; Macdonald, Colin B.; Ruuth, Steven J.
Abstract:
We study the linear stability of the fifth-order Weighted Essentially Non-Oscillatory spatial discretization (WENO5) combined with explicit time stepping applied to the one-dimensional advection equation. We show that it is not necessary for the stability domain of the time integrator to include a part of the imaginary axis. In particular, we show that the combination of WENO5 with either the forward Euler method or a two-stage, second-order Runge-Kutta method is linearly stable provided very small time step-sizes are taken. We also consider fifth-order multistep time discretizations whose stability domains do not include the imaginary axis. These are found to be linearly stable with moderate time steps when combined with WENO5. In particular, the fifth-order extrapolated BDF scheme gave superior results in practice to high-order Runge-Kutta methods whose stability domain includes the imaginary axis. Numerical tests are presented which confirm the analysis. © Springer Science+Business Media, LLC 2010.
Citation:
Motamed M, Macdonald CB, Ruuth SJ (2010) On the Linear Stability of the Fifth-Order WENO Discretization. Journal of Scientific Computing 47: 127–149. Available: http://dx.doi.org/10.1007/s10915-010-9423-9.
Publisher:
Springer Nature
Journal:
Journal of Scientific Computing
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
3-Oct-2010
DOI:
10.1007/s10915-010-9423-9
Type:
Article
ISSN:
0885-7474; 1573-7691
Sponsors:
The work of M. Motamed was partially supported by NSERC Canada.The work of C. B. Macdonald was supported by NSERC Canada, NSF grant number CCF-0321917, and by Award No KUK-C1-013-04 made by King Abdullah University of Science and Technology (KAUST).The work of S.J. Ruuth was partially supported by NSERC Canada.
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Full metadata record

DC FieldValue Language
dc.contributor.authorMotamed, Mohammaden
dc.contributor.authorMacdonald, Colin B.en
dc.contributor.authorRuuth, Steven J.en
dc.date.accessioned2016-02-25T13:52:05Zen
dc.date.available2016-02-25T13:52:05Zen
dc.date.issued2010-10-03en
dc.identifier.citationMotamed M, Macdonald CB, Ruuth SJ (2010) On the Linear Stability of the Fifth-Order WENO Discretization. Journal of Scientific Computing 47: 127–149. Available: http://dx.doi.org/10.1007/s10915-010-9423-9.en
dc.identifier.issn0885-7474en
dc.identifier.issn1573-7691en
dc.identifier.doi10.1007/s10915-010-9423-9en
dc.identifier.urihttp://hdl.handle.net/10754/599059en
dc.description.abstractWe study the linear stability of the fifth-order Weighted Essentially Non-Oscillatory spatial discretization (WENO5) combined with explicit time stepping applied to the one-dimensional advection equation. We show that it is not necessary for the stability domain of the time integrator to include a part of the imaginary axis. In particular, we show that the combination of WENO5 with either the forward Euler method or a two-stage, second-order Runge-Kutta method is linearly stable provided very small time step-sizes are taken. We also consider fifth-order multistep time discretizations whose stability domains do not include the imaginary axis. These are found to be linearly stable with moderate time steps when combined with WENO5. In particular, the fifth-order extrapolated BDF scheme gave superior results in practice to high-order Runge-Kutta methods whose stability domain includes the imaginary axis. Numerical tests are presented which confirm the analysis. © Springer Science+Business Media, LLC 2010.en
dc.description.sponsorshipThe work of M. Motamed was partially supported by NSERC Canada.The work of C. B. Macdonald was supported by NSERC Canada, NSF grant number CCF-0321917, and by Award No KUK-C1-013-04 made by King Abdullah University of Science and Technology (KAUST).The work of S.J. Ruuth was partially supported by NSERC Canada.en
dc.publisherSpringer Natureen
dc.subjectHyperbolic conservation lawsen
dc.subjectLinear stability analysisen
dc.subjectMethod of linesen
dc.subjectMultistep methodsen
dc.subjectRunge-Kutta methodsen
dc.subjectWENOen
dc.titleOn the Linear Stability of the Fifth-Order WENO Discretizationen
dc.typeArticleen
dc.identifier.journalJournal of Scientific Computingen
dc.contributor.institutionSimon Fraser University, Burnaby, Canadaen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
kaust.grant.numberKUK-C1-013-04en
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