On Convergent Schemes for Diffuse Interface Models for Two-Phase Flow of Incompressible Fluids with General Mass Densities

2013 ◽  
Vol 51 (6) ◽  
pp. 3036-3061 ◽  
Author(s):  
G. Grün
Keyword(s):  
Two Phase Flow ◽  
Incompressible Fluids ◽  
Diffuse Interface ◽  
Phase Flow ◽  
Two Phase ◽  
Interface Models ◽  
General Mass

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

2016 ◽  
Vol 19 (5) ◽  
pp. 1473-1502 ◽  
Author(s):  
Günther Grün ◽  
Francisco Guillén-González ◽  
Stefan Metzger
Keyword(s):  
Two Phase Flow ◽  
Diffuse Interface ◽  
Phase Flow ◽  
Interface Model ◽  
Splitting Schemes ◽  
Diffuse Interface Model ◽  
Two Phase ◽  
General Mass ◽  
Two Space Dimensions ◽  
Double Well Potential

AbstractIn 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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