Efficient energy stable schemes for the hydrodynamics coupled phase-field model

Guangpu Zhu, Huangxin Chen, Jun Yao, Shuyu Sun

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Abstract

In this paper, several efficient and energy stable semi-implicit schemes are presented for Cahn-Hilliard phase-field model of two-phase incompressible flows. A scalar auxiliary variable (SAV) approach is implemented to solve the Cahn-Hilliard equation while a splitting method based on pressure stabilization is used to solve Navier-Stokes equation. At each time step, the schemes involve solving only a sequence of linear elliptic equations and computations of phase-field variable, velocity and pressure are totally decoupled. A finite difference method on staggered grids is adopted to spatially discretize the proposed time marching schemes. We rigorously prove the unconditional energy stability for the semi-implicit schemes and fully discrete scheme. Numerical results in both two and three dimensions are obtained, which demonstrate accuracy and effectiveness of the proposed schemes. Using our numerical scheme, we compare the SAV, invariant energy quadratization (IEQ) and stabilization approaches. Bubble rising dynamics and coarsening dynamics are also investigated in detail. The results demonstrate that the SAV approach can be more accurate than the IEQ approach, and the stabilization approach is the least accurate among the three approaches. The energy stability of SAV approach appears better than other approaches at large time steps.
Original languageEnglish (US)
Pages (from-to)82-108
Number of pages27
JournalApplied Mathematical Modelling
Volume70
DOIs
StatePublished - Dec 28 2018

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