A Novel Energy Stable Numerical Scheme for Navier-Stokes-Cahn-Hilliard Two-Phase Flow Model with Variable Densities and Viscosities

Xiaoyu Feng; Jisheng Kou; Shuyu Sun

doi:10.1007/978-3-319-93713-7_9

A Novel Energy Stable Numerical Scheme for Navier-Stokes-Cahn-Hilliard Two-Phase Flow Model with Variable Densities and Viscosities

Xiaoyu Feng, Jisheng Kou, Shuyu Sun^*

^*Corresponding author for this work

Earth Science and Engineering

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

8 Scopus citations

Abstract

A novel numerical scheme including time and spatial discretization is offered for coupled Cahn-Hilliard and Navier-Stokes governing equation system in this paper. Variable densities and viscosities are considered in the numerical scheme. By introducing an intermediate velocity in both Cahn-Hilliard equation and momentum equation, the scheme can keep discrete energy law. A decouple approach based on pressure stabilization is implemented to solve the Navier-Stokes part, while the stabilization or convex splitting method is adopted for the Cahn-Hilliard part. This novel scheme is totally decoupled, linear, unconditionally energy stable for incompressible two-phase flow diffuse interface model. Numerical results demonstrate the validation, accuracy, robustness and discrete energy law of the proposed scheme in this paper.

Original language	English (US)
Title of host publication	Computational Science – ICCS 2018 - 18th International Conference, Proceedings
Editors	Jack Dongarra, Haohuan Fu, Valeria V. Krzhizhanovskaya, Michael Harold Lees, Peter M. Sloot, Yong Shi, Yingjie Tian
Publisher	Springer Verlag
Pages	113-128
Number of pages	16
ISBN (Print)	9783319937120
DOIs	https://doi.org/10.1007/978-3-319-93713-7_9
State	Published - 2018
Event	18th International Conference on Computational Science, ICCS 2018 - Wuxi, China Duration: Jun 11 2018 → Jun 13 2018

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	10862 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	18th International Conference on Computational Science, ICCS 2018
Country/Territory	China
City	Wuxi
Period	06/11/18 → 06/13/18

Bibliographical note

Publisher Copyright:
© 2018, Springer International Publishing AG, part of Springer Nature.

Keywords

Diffuse interface
Energy stable
Two-phase flow

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-319-93713-7_9

Cite this

Feng, X., Kou, J., & Sun, S. (2018). A Novel Energy Stable Numerical Scheme for Navier-Stokes-Cahn-Hilliard Two-Phase Flow Model with Variable Densities and Viscosities. In J. Dongarra, H. Fu, V. V. Krzhizhanovskaya, M. H. Lees, P. M. Sloot, Y. Shi, & Y. Tian (Eds.), Computational Science – ICCS 2018 - 18th International Conference, Proceedings (pp. 113-128). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10862 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-93713-7_9

Feng, Xiaoyu ; Kou, Jisheng ; Sun, Shuyu. / A Novel Energy Stable Numerical Scheme for Navier-Stokes-Cahn-Hilliard Two-Phase Flow Model with Variable Densities and Viscosities. Computational Science – ICCS 2018 - 18th International Conference, Proceedings. editor / Jack Dongarra ; Haohuan Fu ; Valeria V. Krzhizhanovskaya ; Michael Harold Lees ; Peter M. Sloot ; Yong Shi ; Yingjie Tian. Springer Verlag, 2018. pp. 113-128 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "A novel numerical scheme including time and spatial discretization is offered for coupled Cahn-Hilliard and Navier-Stokes governing equation system in this paper. Variable densities and viscosities are considered in the numerical scheme. By introducing an intermediate velocity in both Cahn-Hilliard equation and momentum equation, the scheme can keep discrete energy law. A decouple approach based on pressure stabilization is implemented to solve the Navier-Stokes part, while the stabilization or convex splitting method is adopted for the Cahn-Hilliard part. This novel scheme is totally decoupled, linear, unconditionally energy stable for incompressible two-phase flow diffuse interface model. Numerical results demonstrate the validation, accuracy, robustness and discrete energy law of the proposed scheme in this paper.",

keywords = "Diffuse interface, Energy stable, Two-phase flow",

author = "Xiaoyu Feng and Jisheng Kou and Shuyu Sun",

note = "Publisher Copyright: {\textcopyright} 2018, Springer International Publishing AG, part of Springer Nature.; 18th International Conference on Computational Science, ICCS 2018 ; Conference date: 11-06-2018 Through 13-06-2018",

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doi = "10.1007/978-3-319-93713-7_9",

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Feng, X, Kou, J & Sun, S 2018, A Novel Energy Stable Numerical Scheme for Navier-Stokes-Cahn-Hilliard Two-Phase Flow Model with Variable Densities and Viscosities. in J Dongarra, H Fu, VV Krzhizhanovskaya, MH Lees, PM Sloot, Y Shi & Y Tian (eds), Computational Science – ICCS 2018 - 18th International Conference, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10862 LNCS, Springer Verlag, pp. 113-128, 18th International Conference on Computational Science, ICCS 2018, Wuxi, China, 06/11/18. https://doi.org/10.1007/978-3-319-93713-7_9

A Novel Energy Stable Numerical Scheme for Navier-Stokes-Cahn-Hilliard Two-Phase Flow Model with Variable Densities and Viscosities. / Feng, Xiaoyu; Kou, Jisheng; Sun, Shuyu.
Computational Science – ICCS 2018 - 18th International Conference, Proceedings. ed. / Jack Dongarra; Haohuan Fu; Valeria V. Krzhizhanovskaya; Michael Harold Lees; Peter M. Sloot; Yong Shi; Yingjie Tian. Springer Verlag, 2018. p. 113-128 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10862 LNCS).

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

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T1 - A Novel Energy Stable Numerical Scheme for Navier-Stokes-Cahn-Hilliard Two-Phase Flow Model with Variable Densities and Viscosities

AU - Feng, Xiaoyu

AU - Kou, Jisheng

AU - Sun, Shuyu

PY - 2018

Y1 - 2018

N2 - A novel numerical scheme including time and spatial discretization is offered for coupled Cahn-Hilliard and Navier-Stokes governing equation system in this paper. Variable densities and viscosities are considered in the numerical scheme. By introducing an intermediate velocity in both Cahn-Hilliard equation and momentum equation, the scheme can keep discrete energy law. A decouple approach based on pressure stabilization is implemented to solve the Navier-Stokes part, while the stabilization or convex splitting method is adopted for the Cahn-Hilliard part. This novel scheme is totally decoupled, linear, unconditionally energy stable for incompressible two-phase flow diffuse interface model. Numerical results demonstrate the validation, accuracy, robustness and discrete energy law of the proposed scheme in this paper.

AB - A novel numerical scheme including time and spatial discretization is offered for coupled Cahn-Hilliard and Navier-Stokes governing equation system in this paper. Variable densities and viscosities are considered in the numerical scheme. By introducing an intermediate velocity in both Cahn-Hilliard equation and momentum equation, the scheme can keep discrete energy law. A decouple approach based on pressure stabilization is implemented to solve the Navier-Stokes part, while the stabilization or convex splitting method is adopted for the Cahn-Hilliard part. This novel scheme is totally decoupled, linear, unconditionally energy stable for incompressible two-phase flow diffuse interface model. Numerical results demonstrate the validation, accuracy, robustness and discrete energy law of the proposed scheme in this paper.

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KW - Energy stable

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A2 - Shi, Yong

A2 - Tian, Yingjie

PB - Springer Verlag

T2 - 18th International Conference on Computational Science, ICCS 2018

Y2 - 11 June 2018 through 13 June 2018

ER -

Feng X, Kou J, Sun S. A Novel Energy Stable Numerical Scheme for Navier-Stokes-Cahn-Hilliard Two-Phase Flow Model with Variable Densities and Viscosities. In Dongarra J, Fu H, Krzhizhanovskaya VV, Lees MH, Sloot PM, Shi Y, Tian Y, editors, Computational Science – ICCS 2018 - 18th International Conference, Proceedings. Springer Verlag. 2018. p. 113-128. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-319-93713-7_9

A Novel Energy Stable Numerical Scheme for Navier-Stokes-Cahn-Hilliard Two-Phase Flow Model with Variable Densities and Viscosities

Abstract

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Bibliographical note

Keywords

ASJC Scopus subject areas

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