Publica
Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. Generalized multiscale finite element method for nonNewtonian fluid flow in perforated domain
 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, 2227 June 2016 Melville/NY: AIP Publishing, 2016 (AIP Conference Proceedings 1773) ISBN: 9780735414310 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 nonNewtonian 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 finescale 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.