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Volume 15, Issue 4-5
Penalty-Projection Schemes for the Cahn-Hilliard Navier-Stokes Diffuse Interface Model of Two Phase Flow, and Their Connection to Divergence-Free Coupled Schemes

Leo G. Rebholz, Steven M. Wise & Mengying Xiao

Int. J. Numer. Anal. Mod., 15 (2018), pp. 649-676.

Published online: 2018-04

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  • Abstract

We study and compare fully discrete numerical approximations for the Cahn-Hilliard-Navier-Stokes (CHNS) system of equations that enforce the divergence constraint in different ways, one method via penalization in a projection-type splitting scheme, and the other via strongly divergence-free elements in a fully coupled scheme. We prove a connection between these two approaches, and test the methods against standard ones with several numerical experiments. The tests reveal that CHNS system solutions can be efficiently and accurately computed with penalty-projection methods.

  • Keywords

Cahn-Hilliard-Navier-Stokes system, penalty-projection method and strong divergence-free elements.

  • AMS Subject Headings

35K35, 35Q35, 65M12, 75D06

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

rebholz@clemson.edu (Leo G. Rebholz)

swise1@utk.edu (Steven M. Wise)

mengyix@clemson.ed (Mengying Xiao)

  • BibTex
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  • TXT
@Article{IJNAM-15-649, author = {Rebholz , Leo G.M. Wise , Steven and Xiao , Mengying}, title = {Penalty-Projection Schemes for the Cahn-Hilliard Navier-Stokes Diffuse Interface Model of Two Phase Flow, and Their Connection to Divergence-Free Coupled Schemes}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2018}, volume = {15}, number = {4-5}, pages = {649--676}, abstract = {

We study and compare fully discrete numerical approximations for the Cahn-Hilliard-Navier-Stokes (CHNS) system of equations that enforce the divergence constraint in different ways, one method via penalization in a projection-type splitting scheme, and the other via strongly divergence-free elements in a fully coupled scheme. We prove a connection between these two approaches, and test the methods against standard ones with several numerical experiments. The tests reveal that CHNS system solutions can be efficiently and accurately computed with penalty-projection methods.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/12536.html} }
TY - JOUR T1 - Penalty-Projection Schemes for the Cahn-Hilliard Navier-Stokes Diffuse Interface Model of Two Phase Flow, and Their Connection to Divergence-Free Coupled Schemes AU - Rebholz , Leo G. AU - M. Wise , Steven AU - Xiao , Mengying JO - International Journal of Numerical Analysis and Modeling VL - 4-5 SP - 649 EP - 676 PY - 2018 DA - 2018/04 SN - 15 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/12536.html KW - Cahn-Hilliard-Navier-Stokes system, penalty-projection method and strong divergence-free elements. AB -

We study and compare fully discrete numerical approximations for the Cahn-Hilliard-Navier-Stokes (CHNS) system of equations that enforce the divergence constraint in different ways, one method via penalization in a projection-type splitting scheme, and the other via strongly divergence-free elements in a fully coupled scheme. We prove a connection between these two approaches, and test the methods against standard ones with several numerical experiments. The tests reveal that CHNS system solutions can be efficiently and accurately computed with penalty-projection methods.

Rebholz , Leo G.M. Wise , Steven and Xiao , Mengying. (2018). Penalty-Projection Schemes for the Cahn-Hilliard Navier-Stokes Diffuse Interface Model of Two Phase Flow, and Their Connection to Divergence-Free Coupled Schemes. International Journal of Numerical Analysis and Modeling. 15 (4-5). 649-676. doi:
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