On the group velocity of symmetric and upwind numerical schemes

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dc.contributor.author Karni, Smadar en_US
dc.date.accessioned 2007-04-06T18:39:06Z
dc.date.available 2007-04-06T18:39:06Z
dc.date.issued 1994-06-15 en_US
dc.identifier.citation Karni, Smadar (1994)."On the group velocity of symmetric and upwind numerical schemes." International Journal for Numerical Methods in Fluids 18(11): 1073-1081. <http://hdl.handle.net/2027.42/50210> en_US
dc.identifier.issn 0271-2091 en_US
dc.identifier.issn 1097-0363 en_US
dc.identifier.uri http://hdl.handle.net/2027.42/50210
dc.description.abstract Dissipative numerical approximations to the linear advection equation are considered with respect to their behaviour in the limit of weak dissipation. The context is wave propagation under typical far-field conditions where grids are highly stretched and waves are underresolved. Three classes of schemes are analysed: explicit two-level (i) symmetric and (ii) upwind schemes of optimal accuracy are considered as well as (iii) (symmetric) Runge-Kutta schemes. In the far-field the dissipation of all schemes diminishes. Group speeds of high-frequency modes assume the incorrect sign and may admit ‘backward’ wave propagation if waves are not damped. A fundamental difference arises between the symmetric and upwind cases owing to the different rates at which the dissipation diminishes. In the upwind case, while the amount of damping per time step diminishes, the accumulative damping remains exponential in time. In the symmetric case the accumulative damping tends to unity, yielding in practice non-dissipative schemes. In this light, parasitic modes constitute much less of a problem in the upwind case than in the symmetric case. Numerical tests confirm these findings. en_US
dc.format.extent 419464 bytes
dc.format.extent 3118 bytes
dc.format.mimetype application/pdf
dc.format.mimetype text/plain
dc.publisher John Wiley & Sons, Ltd en_US
dc.subject.other Engineering en_US
dc.subject.other Engineering General en_US
dc.title On the group velocity of symmetric and upwind numerical schemes en_US
dc.type Article en_US
dc.rights.robots IndexNoFollow en_US
dc.subject.hlbsecondlevel Mathematics en_US
dc.subject.hlbtoplevel Science en_US
dc.description.peerreviewed Peer Reviewed en_US
dc.contributor.affiliationum Department of Mathematics, The University of Michigan, Ann Arbor, MI 48109, U.S.A. en_US
dc.description.bitstreamurl http://deepblue.lib.umich.edu/bitstream/2027.42/50210/1/1650181105_ftp.pdf en_US
dc.identifier.doi http://dx.doi.org/10.1002/fld.1650181105 en_US
dc.identifier.source International Journal for Numerical Methods in Fluids en_US
dc.owningcollname Interdisciplinary and Peer-Reviewed
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