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

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/Congresprocedure › Conferentiebijdrage › Academic › peer review

Samenvatting

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.

Originele taal-2	Engels
Titel	Numerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference
Redacteuren	Fred J. Vermolen, Cornelis Vuik
Uitgeverij	Springer
Pagina's	145-153
Aantal pagina's	9
ISBN van geprinte versie	9783030558734
DOI's	https://doi.org/10.1007/978-3-030-55874-1_13
Status	Gepubliceerd - 2021
Evenement	European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2019 - Egmond aan Zee, Nederland Duur: 30 sep. 2019 → 4 okt. 2019

Publicatie series

Naam	Lecture Notes in Computational Science and Engineering
Volume	139
ISSN van geprinte versie	1439-7358
ISSN van elektronische versie	2197-7100

Congres

Congres	European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2019
Land/Regio	Nederland
Stad	Egmond aan Zee
Periode	30/09/19 → 4/10/19

Bibliografische nota

Publisher Copyright:
© 2021, Springer Nature Switzerland AG.

Financiering

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

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

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Citeer dit

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 (editors), Numerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference (blz. 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 (uitgave), Numerical Mathematics and Advanced Applications, ENUMATH 2019 - European Conference. Lecture Notes in Computational Science and Engineering, vol. 139, Springer, blz. 145-153, European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2019, Egmond aan Zee, Nederland, 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. uitgave / Fred J. Vermolen; Cornelis Vuik. Springer, 2021. blz. 145-153 (Lecture Notes in Computational Science and Engineering; Vol. 139).

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/Congresprocedure › Conferentiebijdrage › Academic › peer review

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AU - Lunowa, Stephan Benjamin

AU - Pop, Iuliu Sorin

AU - Koren, Barry

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.

PY - 2021

Y1 - 2021

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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Congres

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