Flux-corrected transport algorithms preserving the eigenvalue range of symmetric tensor quantities

dc.contributor.authorLohmann, Christoph
dc.date.accessioned2017-04-28T11:40:01Z
dc.date.available2017-04-28T11:40:01Z
dc.date.issued2017-04
dc.description.abstractThis paper presents a new approach to constraining the eigenvalue range of symmetric tensors in numerical advection schemes based on the flux-corrected transport (FCT) algorithm and a continuous finite element discretization. In the context of element-based FEM-FCT schemes for scalar conservation laws, the numerical solution is evolved using local extremum diminishing (LED) antidi usive corrections of a low order approximation which is assumed to satisfy the relevant inequality constraints. The application of a limiter to antidi usive element contributions guarantees that the corrected solution remains bounded by the local maxima and minima of the low order predictor. The FCT algorithm to be presented in this paper guarantees the LED property for the largest and smallest eigenvalues of the transported tensor at the low order evolution step. At the antidi usive correction step, this property is preserved by limiting the antidi usive element contributions to all components of the tensor in a synchronized manner. The definition of the element-based correction factors for FCT is based on perturbation bounds for auxiliary tensors which are constrained to be positive semidefinite to enforce the generalized LED condition. The derivation of sharp bounds involves calculating the roots of polynomials of degree up to 3. As inexpensive and numerically stable alternatives, limiting techniques based on appropriate approximations are considered. The ability of the new limiters to enforce local bounds for the eigenvalue range is confirmed by numerical results for 2D advection problems.en
dc.identifier.issn2190-1767
dc.identifier.urihttp://hdl.handle.net/2003/35941
dc.identifier.urihttp://dx.doi.org/10.17877/DE290R-17964
dc.language.isoen
dc.relation.ispartofseriesErgebnisberichte des Instituts für Angewandte Mathematik;564
dc.subjecttensor quantityen
dc.subjectcontinuous Galerkin methoden
dc.subjectflux-corrected transporten
dc.subjectartificial diffusionen
dc.subjectlocal discrete maximum principlesen
dc.subject.ddc610
dc.subject.rswkGalerkin-Methodede
dc.subject.rswkFCT-Verfahrende
dc.titleFlux-corrected transport algorithms preserving the eigenvalue range of symmetric tensor quantitiesen
dc.typeText
dc.type.publicationtypepreprint
dcterms.accessRightsopen access

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