Energy law preserving C-0 finite element schemes for phase field models in two-phase flow computations

Jinsong Hua, Ping Lin, Chun Liu, Qi Wang

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    47 Citations (Scopus)

    Abstract

    We use the idea in [33] to develop the energy law preserving method and compute the diffusive interface (phase-field) models of Allen-Cahn and Cahn-Hilliard type, respectively, governing the motion of two-phase incompressible flows. We discretize these two models using a C-0 finite element in space and a modified midpoint scheme in time. To increase the stability in the pressure variable we treat the divergence free condition by a penalty formulation, under which the discrete energy law can still be derived for these diffusive interface models. Through an example we demonstrate that the energy law preserving method is beneficial for computing these multi-phase flow models. We also demonstrate that when applying the energy law preserving method to the model of Cahn-Hilliard type, un-physical interfacial oscillations may occur. We examine the source of such oscillations and a remedy is presented to eliminate the oscillations. A few two-phase incompressible flow examples are computed to show the good performance of our method. (C) 2011 Elsevier Inc. All rights reserved.

    Original languageEnglish
    Pages (from-to)7115-7131
    Number of pages17
    JournalJournal of Computational Physics
    Volume230
    Issue number19
    DOIs
    Publication statusPublished - 10 Aug 2011

    Keywords

    • Two-phase flow
    • Phase-field method
    • C-0 finite elements
    • Energy law preservation
    • NAVIER-STOKES EQUATIONS
    • SEQUENTIAL REGULARIZATION METHOD
    • BOUNDARY INTEGRAL METHODS
    • BENDING ELASTICITY MODEL
    • 2 INCOMPRESSIBLE FLUIDS
    • FRONT-TRACKING METHOD
    • LIQUID-CRYSTAL FLOWS
    • NUMERICAL-SIMULATION
    • VISCOUS-LIQUIDS
    • DYNAMICS

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