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.
Original language | English (US) |
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Pages (from-to) | 406-426 |
Number of pages | 21 |
Journal | Computer Methods in Applied Mechanics and Engineering |
Volume | 285 |
DOIs | |
State | Published - Mar 2015 |
Bibliographical note
KAUST Repository Item: Exported on 2020-10-01Acknowledgements: The research of T. Chacon Rebollo has been partially funded by Junta de Andalucia "Proyecto de Excelencia" Grant P12-FQM-454.
ASJC Scopus subject areas
- General Physics and Astronomy
- Mechanics of Materials
- Mechanical Engineering
- Computational Mechanics
- Computer Science Applications