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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/25850

Title: A robust, mass conservative scheme for two-phase flow in porous media including Hölder continuous nonlinearities
Authors: Radu, Florin Adrian
Kumar, Kundan
Nordbotten, Jan Martin
Pop, Iuliu Sorin
Issue Date: 2018
Citation: IMA JOURNAL OF NUMERICAL ANALYSIS, (Art N° drx032)
Status: Early View
Abstract: In this work, we present a mass conservative numerical scheme for two-phase flow in porous media. The model for flow consists of two fully coupled, nonlinear equations: a degenerate parabolic equation and an elliptic one. The proposed numerical scheme is based on backward Euler for the temporal discretization and mixed finite element method for the spatial one. A priori stability and error estimates are presented to prove the convergence of the scheme. A monotone increasing, Holder continuous saturation is considered. The convergence of the scheme is naturally dependant on the Holder exponent. The nonlinear systems ¨ within each time step are solved by a robust linearization method, called the L-scheme. This iterative method does not involve any regularization step. The convergence of the L-scheme is rigorously proved under the assumption of a Lipschitz continuous saturation. For the Holder continuous case, a numerical convergence is established. Numerical results (two-dimensional and three-dimensional) are presented to sustain the theoretical findings.
URI: http://hdl.handle.net/1942/25850
DOI: 10.1093/imanum/drx032
ISSN: 0272-4979
Category: A1
Type: Journal Contribution
Appears in Collections: Research publications

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