MULTISCALE METHODS FOR ELLIPTIC PROBLEMS IN POROUS ...

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XVI International Conference on Computational Methods in Water Resources (CMWR-XVI) Ingeniørhuset

MULTISCALE METHODS FOR ELLIPTIC PROBLEMS IN POROUS MEDIA FLOW
Paper
Author:Vegard Kippe <vki@sintef.no> (SINTEF ICT/Applied Mathematics)
Jørg E. Aarnes <jaa@sintef.no> (SINTEF ICT/Applied Mathematics)
Presenter:Vegard Kippe <vki@sintef.no> (SINTEF ICT/Applied Mathematics)
Date: 2006-06-18     Track: Special Sessions     Session: Multiscale methods for flow in porous media
DOI:10.4122/1.1000000481
DOI:10.4122/1.1000000482

We will review three multiscale methods for elliptic equations in porous media flow, namely the Mixed Multiscale Finite Element Method (MsMFEM) [1], the Multiscale Finite Volume Method (MsFVM) [5] and Numerical Subgrid Upscaling (NSU) [2]. Common for the methods is that they are able to produce mass-conservative fine-scale solutions as well as upscaled solutions, and may thus be utilized as either efficient (approximate) fine-scale solvers or robust upscaling methods. We shall consider the methods in both these respects, and compare them to a state-of-the-art upscaling method (Coupled Local-Global Upscaling [3]) combined with a fine-scale reconstruction procedure (Nested Gridding [4]). In order to investigate the properties of the methods, we perform a series of numerical experiments designed to reveal differences with regard to robustness and flexibility. In this process we discover some shortcomings of the methods, and we discuss alternative approaches to remedy these. We will also comment on implementational aspects and present an analysis of the computational effort required by each of the methods. References: 1. J. E. Aarnes, On the use of a mixed multiscale finite element method for greater flexibility and icreased speed or improved accuracy in reservoir simulation, SIAM Multiscale Modeling and Simulation 2 (2004), no. 3, 421­439. 2. T. Arbogast, Numerical subgrid upscaling of two-phase flow in porous media, Numerical Treatment of Multiphase Flows in Porous Media (Z. Chen et. al., ed.), Lecture Notes in Physics, vol. 552, Springer, Berlin, 2000, pp. 35­49. 3. Y. Chen, L. J. Durlofsky, M. Gerritsen, and X. H. Wen, A coupled local-global upscaling approach for simulating flow in highly heterogeneous formations, Advances in Water Resources 26 (2003), 1041­ 1060. 4. Y. Gautier, M. J. Blunt, and M. A. Christie, Nested gridding and streamline-based simulation for fast reservoir performance prediction, Computational Geosciences 3 (1999), 295­320. 5. P. Jenny, S. H. Lee, and H. A. Tchelepi, Multi-scale finite-volume method for elliptic problems in subsurface flow simulation, Journal of Computational Physics (2003), no. 187, 47­67.