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

Francisco Guillén-González & Giordano Tierra

DOI: 10.4208/jcm.1405-m4410

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

Published online: 2014-12

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  • Abstract

In this work, we focus on designing efficient 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-field approach that is able to describe topological transitions like droplet coalescence 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.

  • Copyright

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 efficient 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-field approach that is able to describe topological transitions like droplet coalescence 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, Diffuse-interface phase-field, Cahn-Hilliard, Navier-Stokes, Energy stability, Variable density, Mixed finite element, Splitting scheme. AB -

In this work, we focus on designing efficient 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-field approach that is able to describe topological transitions like droplet coalescence 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 and Giordano Tierra. (2014). 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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