Fully coupled generalized hybrid-mixed finite element approximation of two-phase two-component flow in porous media. Part I: Formulation and properties of the mathematical model

Marchand E, Müller T, Knabner P (2013)

Publication Status: Published

Publication Type: Journal article, Original article

Publication year: 2013

Journal

Computational Geosciences Springer Verlag (Germany)

Publisher: Springer Verlag (Germany)

Book Volume: 17

Pages Range: 431-442

Journal Issue: 2

URI: https://www1.am.uni-erlangen.de/research/publications/Jahr_2013/2013_MarchandMuellerKn_FullyCoupledGeneralizedHybridMixedFinEleApproxPartI

DOI: 10.1007/s10596-013-9341-7

Abstract

This paper is a prequel to that of Marchand et al. (Comput Geosci 16:691-708, 2012), where an efficient and accurate hybrid-mixed finite element approximation for a system of time-dependent nonlinear conservation equations has been formulated, implemented, and tested, which are general enough to represent most of the existing formulations for two-component liquid-gas flow in porous medium with phase exchange, also allowing for any (dis)appearance of one of the phases. Temperature variation is neglected, but capillary effects are included by extended Darcy's law, and Fickian diffusion is taken into account. The efficiency and stability of the numerical method of Lake (1989) relies on an equivalent reformulation of the otherwise commonly used model in terms of new principal variables and subsequent static (flash) equations allowing more generally for any (dis)appearance of one of the phases without the need of variable switching or unphysical quantities. In particular, the formulation in terms of complementarity conditions allows for an efficient and stable solution by the semismooth Newton's method. © 2013 Springer Science+Business Media Dordrecht.

Authors with CRIS profile

Estelle Marchand Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik) Torsten Müller Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik) Peter Knabner Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik)

How to cite

APA:

Marchand, E., Müller, T., & Knabner, P. (2013). Fully coupled generalized hybrid-mixed finite element approximation of two-phase two-component flow in porous media. Part I: Formulation and properties of the mathematical model. Computational Geosciences, 17(2), 431-442. https://dx.doi.org/10.1007/s10596-013-9341-7

MLA:

Marchand, Estelle, Torsten Müller, and Peter Knabner. "Fully coupled generalized hybrid-mixed finite element approximation of two-phase two-component flow in porous media. Part I: Formulation and properties of the mathematical model." Computational Geosciences 17.2 (2013): 431-442.

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