Energy law preserving C0 finite element schemes for phase field models in two-phase flow computations

  • Authors:

  • Jinsong Hua;Ping Lin;Chun Liu;Qi Wang

  • Affiliations:

  • Department of Process and Fluid Flow Technology, Institute for Energy Technology, P.O. Box 40, NO-2027 Kjeller, Norway;Department of Mathematics, University of Dundee, Dundee DD1 4HN, Scotland, United Kingdom;Department of Mathematics, Pennsylvania State University, University Park, PA 18601, USA;Department of Mathematics and NanoCenter at USC, University of South Carolina, Columbia, SC 29208, USA

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2011

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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.