Journal
COMMUNICATIONS IN COMPUTATIONAL PHYSICS
Volume 19, Issue 5, Pages 1473-1502Publisher
GLOBAL SCIENCE PRESS
DOI: 10.4208/cicp.scpde14.39s
Keywords
Two-phase flow; Cahn-Hilliard equation; diffuse interface model; convergence of finite-element schemes; numerical simulation
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Funding
- Deutsche Forschungsgemeinschaft (German Science Foundation) through the Priority Programme Transport processes at fluidic interfaces [1506]
- Ministerio de Econom'ia y Competividad (Spain) [MTM2012-32325]
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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 interfacemodel in [Abels, Garcke, Grun, 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.-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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