Nonconforming multiscale finite element method for Stokes flows in heterogeneous media. Part I: Methodologies and numerical experiments

Muljadi, Bagus P. and Narski, J. and Lozinski, A. and Degond, P. (2015) Nonconforming multiscale finite element method for Stokes flows in heterogeneous media. Part I: Methodologies and numerical experiments. Multiscale Modeling and Simulation: a SIAM Interdisciplinary Journal, 13 (4). pp. 1146-1172. ISSN 1540-3467

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Abstract

The multiscale finite element method (MsFEM) is developed in the vein of the Crouzeix--Raviart element for solving viscous incompressible flows in genuine heterogeneous media. Such flows are relevant in many branches of engineering, often at multiple scales and at regions where analytical representations of the microscopic features of the flows are often unavailable. Full accounts of these problems heavily depend on the geometry of the system under consideration and are computationally expensive. Therefore, a method capable of solving multiscale features of the flow without confining itself to fine scale calculations is sought. The approximation of boundary condition on coarse element edges when computing the multiscale basis functions critically influences the eventual accuracy of any MsFEM approaches. The weakly enforced continuity of Crouzeix--Raviart function space across element edges leads to a natural boundary condition for the multiscale basis functions which relaxes the sensitivity of our method to complex patterns of obstacles exempt from the need to implement any oversampling techniques. Additionally, the application of a penalization method makes it possible to avoid a complex unstructured domain and allows extensive use of simpler Cartesian meshes.

Item Type: Article
Additional Information: c2015 Society for Industrial and Applied Mathematics
Keywords: Crouzeix–Raviart element, Multiscale finite element method, Stokes equations, Penalization method
Schools/Departments: University of Nottingham, UK > Faculty of Engineering > Department of Chemical and Environmental Engineering
Identification Number: 10.1137/14096428X
Depositing User: Muljadi, Bagus
Date Deposited: 19 Sep 2017 10:38
Last Modified: 13 Oct 2017 16:35
URI: http://eprints.nottingham.ac.uk/id/eprint/46423

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