Volume 32, Issue 6
Splitting Schemes for a Navier-Stokes-Cahn-Hilliard Model for Two Fluids with Different Densities

Francisco Guillén-González & Giordano Tierra

J. Comp. Math., 32 (2014), pp. 643-664.

Published online: 2014-12

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  • Abstract

In this work, we focus on designing effcient numerical schemes to approximate a thermodynamically consistent Navier-Stokes/Cahn-Hilliard problem given in [3] modeling the mixture of two incompressible fluids with different densities. The model is based on a diffuse-interface phase-fleld 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 different physical parameters.

  • Keywords

Two-phase flow Diffuse-interface phase-field Cahn-Hilliard Navier-Stokes Energy stability Variable density Mixed finite element Splitting scheme

  • AMS Subject Headings

35Q35 65M60 76D05 76D45 76T10.

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COPYRIGHT: © Global Science Press

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@Article{JCM-32-643, author = {Francisco Guillén-González and Giordano Tierra}, title = {Splitting Schemes for a Navier-Stokes-Cahn-Hilliard Model for Two Fluids with Different Densities}, journal = {Journal of Computational Mathematics}, year = {2014}, volume = {32}, number = {6}, pages = {643--664}, abstract = { In this work, we focus on designing effcient numerical schemes to approximate a thermodynamically consistent Navier-Stokes/Cahn-Hilliard problem given in [3] modeling the mixture of two incompressible fluids with different densities. The model is based on a diffuse-interface phase-fleld 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 different physical parameters. }, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1405-m4410}, url = {http://global-sci.org/intro/article_detail/jcm/8407.html} }
TY - JOUR T1 - Splitting Schemes for a Navier-Stokes-Cahn-Hilliard Model for Two Fluids with Different Densities AU - Francisco Guillén-González & Giordano Tierra JO - Journal of Computational Mathematics VL - 6 SP - 643 EP - 664 PY - 2014 DA - 2014/12 SN - 32 DO - http://doi.org/10.4208/jcm.1405-m4410 UR - https://global-sci.org/intro/article_detail/jcm/8407.html KW - Two-phase flow KW - Diffuse-interface phase-field KW - Cahn-Hilliard KW - Navier-Stokes KW - Energy stability KW - Variable density KW - Mixed finite element KW - Splitting scheme AB - In this work, we focus on designing effcient numerical schemes to approximate a thermodynamically consistent Navier-Stokes/Cahn-Hilliard problem given in [3] modeling the mixture of two incompressible fluids with different densities. The model is based on a diffuse-interface phase-fleld 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 different physical parameters.
Francisco Guillén-González & Giordano Tierra. (1970). Splitting Schemes for a Navier-Stokes-Cahn-Hilliard Model for Two Fluids with Different Densities. Journal of Computational Mathematics. 32 (6). 643-664. doi:10.4208/jcm.1405-m4410
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