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Stabilization of the Spectral Element Method in Convection Dominated Flows by Recovery of Skew-Symmetry
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.ORCID iD: 0000-0001-9627-5903
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.ORCID iD: 0000-0001-7864-3071
2013 (English)In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 57, no 2, 254-277 p.Article in journal (Refereed) Published
Abstract [en]

We investigate stability properties of the spectral element method for advection dominated incompressible flows. In particular, properties of the widely used convective form of the nonlinear term are studied. We remark that problems which are usually associated with the nonlinearity of the governing Navier-Stokes equations also arise in linear scalar transport problems, which implicates advection rather than nonlinearity as a source of difficulty. Thus, errors arising from insufficient quadrature of the convective term, commonly referred to as 'aliasing errors', destroy the skew-symmetric properties of the convection operator. Recovery of skew-symmetry can be efficiently achieved by the use of over-integration. Moreover, we demonstrate that the stability problems are not simply connected to underresolution. We combine theory with analysis of the linear advection-diffusion equation in 2D and simulations of the incompressible Navier-Stokes equations in 2D of thin shear layers at a very high Reynolds number and in 3D of turbulent and transitional channel flow at moderate Reynolds number. For the Navier-Stokes equations, where the divergence-free constraint needs to be enforced iteratively to a certain accuracy, small divergence errors can be detrimental to the stability of the method and it is therefore advised to use additional stabilization (e.g. so-called filter-based stabilization, spectral vanishing viscosity or entropy viscosity) in order to assure a stable spectral element method.

Place, publisher, year, edition, pages
2013. Vol. 57, no 2, 254-277 p.
Keyword [en]
Spectral element method (SEM), Stability, Over-integration, Skew-symmetry
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:kth:diva-133520DOI: 10.1007/s10915-013-9704-1ISI: 000325138400002Scopus ID: 2-s2.0-84885471926OAI: oai:DiVA.org:kth-133520DiVA: diva2:662395
Funder
Swedish Research CouncilKnut and Alice Wallenberg FoundationSwedish e‐Science Research Center
Note

QC 20131107

Available from: 2013-11-07 Created: 2013-11-06 Last updated: 2017-12-06Bibliographically approved

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Schlatter, PhilippHenningson, Dan S.

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MechanicsLinné Flow Center, FLOWSeRC - Swedish e-Science Research CentreStability, Transition and Control
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