Local-global splitting for spatiotemporal-adaptive multiscale methods

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Etat: Public
Version: de l'auteur
ID Serval
serval:BIB_1DFF2DD6BAF4
Type
Article: article d'un périodique ou d'un magazine.
Collection
Publications
Institution
Titre
Local-global splitting for spatiotemporal-adaptive multiscale methods
Périodique
Journal of Computational Physics
Auteur(s)
Tomin P., Lunati I.
ISSN
0021-9991 (Print)
Statut éditorial
Publié
Date de publication
2015
Peer-reviewed
Oui
Volume
280
Pages
214-231
Langue
anglais
Résumé
We present a novel spatiotemporal-adaptive Multiscale Finite Volume (MsFV) method, which is based on the natural idea that the global coarse-scale problem has longer characteristic time than the local fine-scale problems. As a consequence, the global problem can be solved with larger time steps than the local problems. In contrast to the pressure-transport splitting usually employed in the standard MsFV approach, we propose to start directly with a local-global splitting that allows to locally retain the original degree of coupling. This is crucial for highly non-linear systems or in the presence of physical instabilities. To obtain an accurate and efficient algorithm, we devise new adaptive criteria for global update that are based on changes of coarse-scale quantities rather than on fine-scale quantities, as it is routinely done before in the adaptive MsFV method. By means of a complexity analysis we show that the adaptive approach gives a noticeable speed-up with respect to the standard MsFV algorithm. In particular, it is efficient in case of large upscaling factors, which is important for multiphysics problems. Based on the observation that local time stepping acts as a smoother, we devise a self-correcting algorithm which incorporates the information from previous times to improve the quality of the multiscale approximation. We present results of multiphase flow simulations both for Darcy-scale and multiphysics (hybrid) problems, in which a local pore-scale description is combined with a global Darcy-like description. The novel spatiotemporal-adaptive multiscale method based on the local-global splitting is not limited to porous media flow problems, but it can be extended to any system described by a set of conservation equations.
Mots-clé
Multiscale methods, Spatiotemporal adaptivity, Local-global splitting, Multiphysics
Open Access
Oui
Création de la notice
07/10/2014 21:30
Dernière modification de la notice
20/08/2019 12:54
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