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A phase-field method for three-phase flows with icing

Zhang, Wenqiang; Shahmardi, Armin; Choi, Kwing-so; Tammisola, Outi; Brandt, Luca; Mao, Xuerui

A phase-field method for three-phase flows with icing Thumbnail


Wenqiang Zhang

Armin Shahmardi

Professor of Fluid Mechanics

Outi Tammisola

Luca Brandt

Xuerui Mao


A numerical scheme to simulate three-phase fluid flows with phase change is proposed. By combining the Cahn-Hilliard model for water-air interface, Allen-Cahn equation for ice and fluid and Navier-Stokes equation for momentum, we solve the evolution of the water-air interface and water-ice interface simultaneously, including the volume expansion associated with solidification and due to the density difference between water and ice. Unlike existing schemes assuming a divergence-free flow field, the proposed continuous formulation allows for density changes while ensuring mass conservation. A Poisson equation for the pressure field is derived from mass conservation with constant coefficients, which can efficiently be solved without any pre-conditioning. The results demonstrate that the volume expansion during the ice formation and the subsequent motion of the water-air interface are successfully captured. A parametric study is carried out to examine the dependence of the icing on different physical and numerical parameters. Computations with flow disturbance of different amplitudes demonstrate the robustness of the computational scheme and the uniqueness of the solution over the parameters considered.


Zhang, W., Shahmardi, A., Choi, K., Tammisola, O., Brandt, L., & Mao, X. (2022). A phase-field method for three-phase flows with icing. Journal of Computational Physics, 458, Article 111104.

Journal Article Type Article
Acceptance Date Feb 25, 2022
Online Publication Date Mar 4, 2022
Publication Date Jun 1, 2022
Deposit Date Mar 17, 2022
Publicly Available Date Mar 5, 2023
Journal Journal of Computational Physics
Print ISSN 0021-9991
Electronic ISSN 1090-2716
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 458
Article Number 111104
Keywords Computer Science Applications; Physics and Astronomy (miscellaneous); Applied Mathematics; Computational Mathematics; Modeling and Simulation; Numerical Analysis
Public URL
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Additional Information This article is maintained by: Elsevier; Article Title: A phase-field method for three-phase flows with icing; Journal Title: Journal of Computational Physics; CrossRef DOI link to publisher maintained version:; Content Type: article; Copyright: © 2022 Elsevier Inc. All rights reserved.


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