@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 = {<p style="text-align: justify;">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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.scpde14.39s},
url = {http://global-sci.org/intro/article_detail/cicp/11139.html}
}