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Generalized multiscale finite element method for non-Newtonian fluid flow in perforated domain

 
: Chung, E.T.; Iliev, O.; Vasilyeva, M.V.

:

Todorov, M.:
Application of mathematics in technical and natural sciences : 8th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS'16; Albena, Bulgaria, 22-27 June 2016
Melville/NY: AIP Publishing, 2016 (AIP Conference Proceedings 1773)
ISBN: 978-0-7354-1431-0
Art. 100001, 9 pp.
International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences (AMiTaNS) <8, 2016, Albena/Bulgaria>
English
Conference Paper
Fraunhofer ITWM ()

Abstract
In this work, we consider a non-Newtonian fluid flow in perforated domains. Fluid flow in perforated domains have a multiscale nature and solution techniques for such problems require high resolution. In particular, the discretization needs to honor the irregular boundaries of perforations. This gives rise to a fine-scale problems with many degrees of freedom which can be very expensive to solve. In this work, we develop a multiscale approach that attempt to solve such problems on a coarse grid by constructing multiscale basis functions. We follow Generalized Multiscale Finite Element Method (GMsFEM) [1, 2] and develop a multiscale procedure where we identify multiscale basis functions in each coarse block using snapshot space and local spectral problems [3, 4]. We show that with a few basis functions in each coarse block, one can accurately approximate the solution, where each coarse block can contain many small inclusions.

: http://publica.fraunhofer.de/documents/N-444972.html