On Fully Decoupled, Convergent Schemes for Diffuse Interface Models for Two-Phase Flow with General Mass Densities. (17th May 2016)

• Record Type: Journal Article
• Authors: Grün, Günther; Guillén-González, Francisco; Metzger, Stefan
• Is Part Of: Communications in computational physics. Volume 19:Number 5(2016:May)
• Page Start: 1473
• Page End: 1502
• Publication Date: 2016-05-17
• Subjects: 35Q35, -- 65M60, -- 65M22, -- 65M12, -- 76D05, -- 76T10; Two-phase flow, -- Cahn-Hilliard equation, -- diffuse interface model, -- convergence of finite-element schemes, -- numerical simulation; Mathematical physics -- Data processing -- Periodicals; Physics -- Data processing -- Periodicals; 530.150285
• DOI: 10.4208/cicp.scpde14.39s
• Languages: English
• ISSNs: 1815-2406

Abstract

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.