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dc.contributor.authorKleiser, Leonhard-
dc.contributor.authorWilhelm, Dirk-
dc.date.accessioned2018-12-11T15:33:06Z-
dc.date.available2018-12-11T15:33:06Z-
dc.date.issued2001-11-
dc.identifier.issn0021-9991de_CH
dc.identifier.issn1090-2716de_CH
dc.identifier.urihttps://digitalcollection.zhaw.ch/handle/11475/13735-
dc.description.abstractWe show that for the PN−PN−2 spectral element method, in which velocity and pressure are approximated by polynomials of order N and N−2, respectively, numerical instabilities can occur in the spatially discretized Navier–Stokes equations. Both a staggered and nonstaggered arrangement of the N−2 pressure points are considered. These instabilities can be masked by viscous damping at low Reynolds numbers. We demonstrate that the instabilities depend on the formulation of the nonlinear term. The numerical discretization is stable for the convective form but unstable for the divergence and the skew-symmetric form. Further numerical analysis indicates that this instability is not caused by nonlinear effects, since it occurs for linearized systems as well. An eigenvalue analysis of the fully discretized system shows that an instability is introduced by the formulation of the nonlinear term. We demonstrate that the instability is related to the divergence error of the computed solution at those velocity points at which the continuity equation is not enforced.de_CH
dc.language.isoende_CH
dc.publisherElsevierde_CH
dc.relation.ispartofJournal of Computational Physicsde_CH
dc.rightsLicence according to publishing contractde_CH
dc.subject.ddc510: Mathematikde_CH
dc.titleStability analysis for different formulations of the nonlinear term in PN−PN−2 spectral element discretizations of the navier–stokes equationsde_CH
dc.typeBeitrag in wissenschaftlicher Zeitschriftde_CH
dcterms.typeTextde_CH
zhaw.departementSchool of Engineeringde_CH
dc.identifier.doi10.1006/jcph.2001.6912de_CH
zhaw.funding.euNode_CH
zhaw.issue1de_CH
zhaw.originated.zhawNode_CH
zhaw.pages.end326de_CH
zhaw.pages.start306de_CH
zhaw.publication.statuspublishedVersionde_CH
zhaw.volume174de_CH
zhaw.publication.reviewPeer review (Publikation)de_CH
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Kleiser, L., & Wilhelm, D. (2001). Stability analysis for different formulations of the nonlinear term in PN−PN−2 spectral element discretizations of the navier–stokes equations. Journal of Computational Physics, 174(1), 306–326. https://doi.org/10.1006/jcph.2001.6912
Kleiser, L. and Wilhelm, D. (2001) ‘Stability analysis for different formulations of the nonlinear term in PN−PN−2 spectral element discretizations of the navier–stokes equations’, Journal of Computational Physics, 174(1), pp. 306–326. Available at: https://doi.org/10.1006/jcph.2001.6912.
L. Kleiser and D. Wilhelm, “Stability analysis for different formulations of the nonlinear term in PN−PN−2 spectral element discretizations of the navier–stokes equations,” Journal of Computational Physics, vol. 174, no. 1, pp. 306–326, Nov. 2001, doi: 10.1006/jcph.2001.6912.
KLEISER, Leonhard und Dirk WILHELM, 2001. Stability analysis for different formulations of the nonlinear term in PN−PN−2 spectral element discretizations of the navier–stokes equations. Journal of Computational Physics. November 2001. Bd. 174, Nr. 1, S. 306–326. DOI 10.1006/jcph.2001.6912
Kleiser, Leonhard, and Dirk Wilhelm. 2001. “Stability Analysis for Different Formulations of the Nonlinear Term in PN−PN−2 Spectral Element Discretizations of the Navier–Stokes Equations.” Journal of Computational Physics 174 (1): 306–26. https://doi.org/10.1006/jcph.2001.6912.
Kleiser, Leonhard, and Dirk Wilhelm. “Stability Analysis for Different Formulations of the Nonlinear Term in PN−PN−2 Spectral Element Discretizations of the Navier–Stokes Equations.” Journal of Computational Physics, vol. 174, no. 1, Nov. 2001, pp. 306–26, https://doi.org/10.1006/jcph.2001.6912.


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