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

On Fully Decoupled, Convergent Schemes for Diffuse Interface Models for Two-Phase Flow with General Mass Densities
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Year:    2016

Communications in Computational Physics, Vol. 19 (2016), Iss. 5 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.scpde14.39s

Communications in Computational Physics, Vol. 19 (2016), Iss. 5 : pp. 1473–1502

Published online:    2016-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    30

Keywords:   

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