Volume 19, Issue 5
On Fully Decoupled, Convergent Schemes for Diffuse Interface Models for Two-Phase Flow with General Mass Densities

Günther Grün, Francisco Guillén-González & Stefan Metzger

Commun. Comput. Phys., 19 (2016), pp. 1473-1502.

Published online: 2018-04

Preview Full PDF 195 1085
Export citation
  • Abstract

In the first part, we study the convergence of discrete solutions to splitting schemes for two-phase flow with different mass densities suggested in [Guillen-Gonzalez, Tierra, J. Comput. Math. (6)2014]. They have been formulated for the diffuse interface model in [Abels, Garcke, Grün, M3AS, 2012, DOI: 10.1142/S0218202511500138] which is consistent with thermodynamics. Our technique covers various discretization methods for phase-field energies, ranging from convex-concave splitting to difference quotient approaches for the double-well potential. In the second part of the paper, numerical experiments are presented in two space dimensions to identify discretizations of Cahn-Hilliard energies which are φ-stable and which do not reduce the acceleration of falling droplets. Finally, 3d simulations in axial symmetric geometries are shown to underline even more the full practicality of the approach.

  • Keywords

  • AMS Subject Headings

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{CiCP-19-1473, author = {}, title = {On Fully Decoupled, Convergent Schemes for Diffuse Interface Models for Two-Phase Flow with General Mass Densities}, journal = {Communications in Computational Physics}, year = {2018}, volume = {19}, number = {5}, pages = {1473--1502}, abstract = {

In the first part, we study the convergence of discrete solutions to splitting schemes for two-phase flow with different mass densities suggested in [Guillen-Gonzalez, Tierra, J. Comput. Math. (6)2014]. They have been formulated for the diffuse interface model in [Abels, Garcke, Grün, M3AS, 2012, DOI: 10.1142/S0218202511500138] which is consistent with thermodynamics. Our technique covers various discretization methods for phase-field energies, ranging from convex-concave splitting to difference quotient approaches for the double-well potential. In the second part of the paper, numerical experiments are presented in two space dimensions to identify discretizations of Cahn-Hilliard energies which are φ-stable and which do not reduce the acceleration of falling droplets. Finally, 3d simulations in axial symmetric geometries are shown to underline even more the full practicality of the approach.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.scpde14.39s}, url = {http://global-sci.org/intro/article_detail/cicp/11139.html} }
TY - JOUR T1 - On Fully Decoupled, Convergent Schemes for Diffuse Interface Models for Two-Phase Flow with General Mass Densities JO - Communications in Computational Physics VL - 5 SP - 1473 EP - 1502 PY - 2018 DA - 2018/04 SN - 19 DO - http://doi.org/10.4208/cicp.scpde14.39s UR - https://global-sci.org/intro/article_detail/cicp/11139.html KW - AB -

In the first part, we study the convergence of discrete solutions to splitting schemes for two-phase flow with different mass densities suggested in [Guillen-Gonzalez, Tierra, J. Comput. Math. (6)2014]. They have been formulated for the diffuse interface model in [Abels, Garcke, Grün, M3AS, 2012, DOI: 10.1142/S0218202511500138] which is consistent with thermodynamics. Our technique covers various discretization methods for phase-field energies, ranging from convex-concave splitting to difference quotient approaches for the double-well potential. In the second part of the paper, numerical experiments are presented in two space dimensions to identify discretizations of Cahn-Hilliard energies which are φ-stable and which do not reduce the acceleration of falling droplets. Finally, 3d simulations in axial symmetric geometries are shown to underline even more the full practicality of the approach.

Günther Grün, Francisco Guillén-González & Stefan Metzger. (2020). On Fully Decoupled, Convergent Schemes for Diffuse Interface Models for Two-Phase Flow with General Mass Densities. Communications in Computational Physics. 19 (5). 1473-1502. doi:10.4208/cicp.scpde14.39s
Copy to clipboard
The citation has been copied to your clipboard