A variational multi-scale method with spectral approximation of the sub-scales: Application to the 1D advection-diffusion equations

Handle URI:
http://hdl.handle.net/10754/564075
Title:
A variational multi-scale method with spectral approximation of the sub-scales: Application to the 1D advection-diffusion equations
Authors:
Chacón Rebollo, Tomás; Dia, Ben Mansour
Abstract:
This paper introduces a variational multi-scale method where the sub-grid scales are computed by spectral approximations. It is based upon an extension of the spectral theorem to non necessarily self-adjoint elliptic operators that have an associated base of eigenfunctions which are orthonormal in weighted L2 spaces. This allows to element-wise calculate the sub-grid scales by means of the associated spectral expansion. We propose a feasible VMS-spectral method by truncation of this spectral expansion to a finite number of modes. We apply this general framework to the convection-diffusion equation, by analytically computing the family of eigenfunctions. We perform a convergence and error analysis. We also present some numerical tests that show the stability of the method for an odd number of spectral modes, and an improvement of accuracy in the large resolved scales, due to the adding of the sub-grid spectral scales.
KAUST Department:
Center for Uncertainty Quantification in Computational Science and Engineering (SRI-UQ); Applied Mathematics and Computational Science Program
Publisher:
Elsevier BV
Journal:
Computer Methods in Applied Mechanics and Engineering
Issue Date:
Mar-2015
DOI:
10.1016/j.cma.2014.11.025
Type:
Article
ISSN:
00457825
Sponsors:
The research of T. Chacon Rebollo has been partially funded by Junta de Andalucia "Proyecto de Excelencia" Grant P12-FQM-454.
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program

Full metadata record

DC FieldValue Language
dc.contributor.authorChacón Rebollo, Tomásen
dc.contributor.authorDia, Ben Mansouren
dc.date.accessioned2015-08-03T12:31:01Zen
dc.date.available2015-08-03T12:31:01Zen
dc.date.issued2015-03en
dc.identifier.issn00457825en
dc.identifier.doi10.1016/j.cma.2014.11.025en
dc.identifier.urihttp://hdl.handle.net/10754/564075en
dc.description.abstractThis paper introduces a variational multi-scale method where the sub-grid scales are computed by spectral approximations. It is based upon an extension of the spectral theorem to non necessarily self-adjoint elliptic operators that have an associated base of eigenfunctions which are orthonormal in weighted L2 spaces. This allows to element-wise calculate the sub-grid scales by means of the associated spectral expansion. We propose a feasible VMS-spectral method by truncation of this spectral expansion to a finite number of modes. We apply this general framework to the convection-diffusion equation, by analytically computing the family of eigenfunctions. We perform a convergence and error analysis. We also present some numerical tests that show the stability of the method for an odd number of spectral modes, and an improvement of accuracy in the large resolved scales, due to the adding of the sub-grid spectral scales.en
dc.description.sponsorshipThe research of T. Chacon Rebollo has been partially funded by Junta de Andalucia "Proyecto de Excelencia" Grant P12-FQM-454.en
dc.publisherElsevier BVen
dc.subjectAdvection-diffusionen
dc.subjectSpectral approximationen
dc.subjectStabilizationen
dc.subjectVariational multiscaleen
dc.titleA variational multi-scale method with spectral approximation of the sub-scales: Application to the 1D advection-diffusion equationsen
dc.typeArticleen
dc.contributor.departmentCenter for Uncertainty Quantification in Computational Science and Engineering (SRI-UQ)en
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.identifier.journalComputer Methods in Applied Mechanics and Engineeringen
dc.contributor.institutionDepartamento EDAN and IMUS, University of Sevilla, Facultad de Matemáticas, C/ Tarfia, s/nSevilla, Spainen
dc.contributor.institutionUniversity of Bordeaux, IPB-I2M, Franceen
kaust.authorDia, Ben Mansouren
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