A robust, mass conservative scheme for two-phase flow in porous media including Hölder continuous nonlinearities

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 temp...

Full description

Saved in:
Bibliographic Details
Published in:IMA journal of numerical analysis 2018-04, Vol.38 (2), p.884-920
Main Authors: Radu, Florin A, Kumar, Kundan, Nordbotten, Jan M, Pop, Iuliu S
Format: Article
Language:English
Subjects:
Matematik
Mathematics
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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, Hölder continuous saturation is considered. The convergence of the scheme is naturally dependant on the Hölder 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 Hölder continuous case, a numerical convergence is established. Numerical results (two-dimensional and three-dimensional) are presented to sustain the theoretical findings.
ISSN:0272-4979
1464-3642
1464-3642
DOI:10.1093/imanum/drx032