A conservative phase field method for solving incompressible two-phase flows

In this paper a conservative phase-field method based on the work of Sun and Beckermann [Y. Sun, C. Beckermann, Sharp interface tracking using the phase-field equation, J. Comput. Phys. 220 (2007) 626–653] for solving the two- and three-dimensional two-phase incompressible Navier–Stokes equations is...

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Bibliographic Details
Published in:Journal of computational physics 2011, Vol.230 (1), p.185-204
Main Authors: Chiu, Pao-Hsiung, Lin, Yan-Ting
Format: Article
Language:English
Subjects:
Allen–Cahn equation
Computational techniques
Conservative phase-field method
Dispersion-relation-preserving
Exact sciences and technology
Helmholtz smoother
Mathematical methods in physics
Physics
Two-phase flow
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Summary:In this paper a conservative phase-field method based on the work of Sun and Beckermann [Y. Sun, C. Beckermann, Sharp interface tracking using the phase-field equation, J. Comput. Phys. 220 (2007) 626–653] for solving the two- and three-dimensional two-phase incompressible Navier–Stokes equations is proposed. The present method can preserve the total mass as the Cahn–Hilliard equation, but the calculation and implementation are much simpler than that. The dispersion-relation-preserving schemes are utilized for the advection terms while the Helmholtz smoother is applied to compute the surface-tension force term. To verify the proposed method, several benchmarks are examined and shown to have good agreements with previous results. It also shows that the satisfactions of mass conservations are guaranteed.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2010.09.021