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

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  • 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 [GuillenGonzalez, Tierra, J.Comput.Math. (6)2014]. They have been formulated for the diffuse interface model in [Abels, Garcke, Gr ¨un, 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.

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@Article{CiCP-19-1473, author = {Günther Grün, Francisco Guillén-González and Stefan Metzger}, 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 [GuillenGonzalez, Tierra, J.Comput.Math. (6)2014]. They have been formulated for the diffuse interface model in [Abels, Garcke, Gr ¨un, 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} }
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