A Linear Domain Decomposition Method for Non-equilibrium Two-Phase Flow Models

Stephan Benjamin Lunowa; Iuliu Sorin Pop; Barry Koren

doi:10.1007/978-3-030-55874-1_13

A Linear Domain Decomposition Method for Non-equilibrium Two-Phase Flow Models

Stephan Benjamin Lunowa, Iuliu Sorin Pop, Barry Koren

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

Abstract

We consider a model for two-phase flow in a porous medium posed in a domain consisting of two adjacent regions. The model includes dynamic capillarity and hysteresis. At the interface between adjacent subdomains, the continuity of the normal fluxes and pressures is assumed. For finding the semi-discrete solutions after temporal discretization by the θ-scheme, we proposed an iterative scheme. It combines a (fixed-point) linearization scheme and a non-overlapping domain decomposition method. This article describes the scheme, its convergence and a numerical study confirming this result. The convergence of the iteration towards the solution of the semi-discrete equations is proved independently of the initial guesses and of the spatial discretization, and under some mild constraints on the time step. Hence, this scheme is robust and can be easily implemented for realistic applications.

Original language	English
Title of host publication	Numerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference
Editors	Fred J. Vermolen, Cornelis Vuik
Publisher	Springer
Pages	145-153
Number of pages	9
ISBN (Print)	9783030558734
DOIs	https://doi.org/10.1007/978-3-030-55874-1_13
Publication status	Published - 2021
Event	European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2019 - Egmond aan Zee, Netherlands Duration: 30 Sept 2019 → 4 Oct 2019

Publication series

Name	Lecture Notes in Computational Science and Engineering
Volume	139
ISSN (Print)	1439-7358
ISSN (Electronic)	2197-7100

Conference

Conference	European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2019
Country/Territory	Netherlands
City	Egmond aan Zee
Period	30/09/19 → 4/10/19

Bibliographical note

Funding Information:
Acknowledgments This work was supported by Eindhoven University of Technology, Has-selt University (Project BOF17NI01) and the Research Foundation Flanders (FWO, Project G051418N).

Publisher Copyright:
© 2021, Springer Nature Switzerland AG.

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10.1007/978-3-030-55874-1_13

Cite this

Lunowa, S. B., Pop, I. S., & Koren, B. (2021). A Linear Domain Decomposition Method for Non-equilibrium Two-Phase Flow Models. In F. J. Vermolen, & C. Vuik (Eds.), Numerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference (pp. 145-153). (Lecture Notes in Computational Science and Engineering; Vol. 139). Springer. https://doi.org/10.1007/978-3-030-55874-1_13

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title = "A Linear Domain Decomposition Method for Non-equilibrium Two-Phase Flow Models",

abstract = "We consider a model for two-phase flow in a porous medium posed in a domain consisting of two adjacent regions. The model includes dynamic capillarity and hysteresis. At the interface between adjacent subdomains, the continuity of the normal fluxes and pressures is assumed. For finding the semi-discrete solutions after temporal discretization by the θ-scheme, we proposed an iterative scheme. It combines a (fixed-point) linearization scheme and a non-overlapping domain decomposition method. This article describes the scheme, its convergence and a numerical study confirming this result. The convergence of the iteration towards the solution of the semi-discrete equations is proved independently of the initial guesses and of the spatial discretization, and under some mild constraints on the time step. Hence, this scheme is robust and can be easily implemented for realistic applications.",

author = "Lunowa, {Stephan Benjamin} and Pop, {Iuliu Sorin} and Barry Koren",

note = "Funding Information: Acknowledgments This work was supported by Eindhoven University of Technology, Has-selt University (Project BOF17NI01) and the Research Foundation Flanders (FWO, Project G051418N). Publisher Copyright: {\textcopyright} 2021, Springer Nature Switzerland AG.; European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2019 ; Conference date: 30-09-2019 Through 04-10-2019",

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Lunowa, SB, Pop, IS & Koren, B 2021, A Linear Domain Decomposition Method for Non-equilibrium Two-Phase Flow Models. in FJ Vermolen & C Vuik (eds), Numerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference. Lecture Notes in Computational Science and Engineering, vol. 139, Springer, pp. 145-153, European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2019, Egmond aan Zee, Netherlands, 30/09/19. https://doi.org/10.1007/978-3-030-55874-1_13

A Linear Domain Decomposition Method for Non-equilibrium Two-Phase Flow Models. / Lunowa, Stephan Benjamin; Pop, Iuliu Sorin ; Koren, Barry.
Numerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference. ed. / Fred J. Vermolen; Cornelis Vuik. Springer, 2021. p. 145-153 (Lecture Notes in Computational Science and Engineering; Vol. 139).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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N1 - Funding Information: Acknowledgments This work was supported by Eindhoven University of Technology, Has-selt University (Project BOF17NI01) and the Research Foundation Flanders (FWO, Project G051418N). Publisher Copyright: © 2021, Springer Nature Switzerland AG.

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N2 - We consider a model for two-phase flow in a porous medium posed in a domain consisting of two adjacent regions. The model includes dynamic capillarity and hysteresis. At the interface between adjacent subdomains, the continuity of the normal fluxes and pressures is assumed. For finding the semi-discrete solutions after temporal discretization by the θ-scheme, we proposed an iterative scheme. It combines a (fixed-point) linearization scheme and a non-overlapping domain decomposition method. This article describes the scheme, its convergence and a numerical study confirming this result. The convergence of the iteration towards the solution of the semi-discrete equations is proved independently of the initial guesses and of the spatial discretization, and under some mild constraints on the time step. Hence, this scheme is robust and can be easily implemented for realistic applications.

AB - We consider a model for two-phase flow in a porous medium posed in a domain consisting of two adjacent regions. The model includes dynamic capillarity and hysteresis. At the interface between adjacent subdomains, the continuity of the normal fluxes and pressures is assumed. For finding the semi-discrete solutions after temporal discretization by the θ-scheme, we proposed an iterative scheme. It combines a (fixed-point) linearization scheme and a non-overlapping domain decomposition method. This article describes the scheme, its convergence and a numerical study confirming this result. The convergence of the iteration towards the solution of the semi-discrete equations is proved independently of the initial guesses and of the spatial discretization, and under some mild constraints on the time step. Hence, this scheme is robust and can be easily implemented for realistic applications.

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A Linear Domain Decomposition Method for Non-equilibrium Two-Phase Flow Models

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