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Journal of Computational Mathematics ›› 2014, Vol. 32 ›› Issue (6): 643-664.DOI: 10.4208/jcm.1405-m4410

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SPLITTING SCHEMES FOR A NAVIER-STOKES-CAHN-HILLIARD MODEL FOR TWO FLUIDS WITH DIFFERENT DENSITIES

Francisco Guillén-González1, Giordano Tier2,3   

  1. 1. Departamento de Ecuaciones Diferenciales y An alisis Num erico and IMUS, Universidad de Sevilla, 41012 Seville, Spain;
    2. Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN 46556, USA;
    3. Current address: Mathematical Institute, Faculty of Mathematics and Physics, Charles University, Prague 8, 186 75, Czech Republic
  • Received:2013-07-12 Revised:2014-04-03 Online:2014-11-15 Published:2014-09-03
  • Supported by:

    This work has been partially supported by MTM2009-12927 and MTM2012-32325 (Ministerio de Econom a y Competitividad, Spain). G. Tierra has also been partially supported by NIH 1 R01 GM095959-01A1 (United States).

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Francisco Guillén-González, Giordano Tier. SPLITTING SCHEMES FOR A NAVIER-STOKES-CAHN-HILLIARD MODEL FOR TWO FLUIDS WITH DIFFERENT DENSITIES[J]. Journal of Computational Mathematics, 2014, 32(6): 643-664.

In this work, we focus on designing e cient numerical schemes to approximate a thermodynamically consistent Navier-Stokes/Cahn-Hilliard problem given in [3] modeling the mixture of two incompressible uids with di erent densities. The model is based on a di use-interface phase-eld approach that is able to describe topological transitions like droplet coalescense or droplet break-up in a natural way. We present a splitting scheme, decoupling computations of the Navier-Stokes part from the Cahn-Hilliard one, which is unconditionally energy-stable up to the choice of the potential approximation. Some numerical experiments are carried out to validate the correctness and the accuracy of the scheme, and to study the sensitivity of the scheme with respect to di erent physical parameters.
Key words: Two-phase flow, Di use-interface phase-eld, Cahn-Hilliard, Navier-Stokes, Energy stability, Variable density, Mixed nite element, Splitting scheme

CLC Number: 

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