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

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

4 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
Publisher	Springer Nature
Pages	113-128
Number of pages	16
ISBN (Print)	9783319937120
DOIs	https://doi.org/10.1007/978-3-319-93713-7_9
State	Published - Jun 12 2018

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

https://repository.kaust.edu.sa/bitstream/10754/628339/1/ICCS2018-Paper%20136%20Final.pdf

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

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.",

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AU - Feng, Xiaoyu

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AU - Sun, Shuyu

N1 - KAUST Repository Item: Exported on 2021-02-23

PY - 2018/6/12

Y1 - 2018/6/12

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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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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