On Fully Decoupled, Convergent Schemes for Diffuse Interface Models for Two-Phase Flow with General Mass Densities (Communications in Computational Physics, 2020)
In the first part, we study the convergence of discrete solutions to splittingschemes for two-phase flow with different mass densities suggested in [Guillen-Gonzalez,Tierra, J. Comput. Math. (6)2014]. They have been formulated for the diffuseinterface model in [Abels, Garcke, Grün, M3AS, 2012, DOI: 10.1142/S0218202511500138]which is consistent with thermodynamics. Our technique covers various discretizationmethods for phase-field energies, ranging from convex-concave splitting to differencequotient approaches for the double-well potential. In the second part of the paper, numericalexperiments are presented in two space dimensions to identify discretizationsof Cahn-Hilliard energies which are φ-stable and which do not reduce the accelerationof falling droplets. Finally, 3d simulations in axial symmetric geometries are shown tounderline even more the full practicality of the approach.