MATHICSE-GroupDede', LucaGarcke, HaraldLam, Kei Fong2019-06-252019-06-252019-06-252017-01-0110.5075/epfl-MATHICSE-267612https://infoscience.epfl.ch/handle/20.500.14299/158499Topology changes in multi-phase fluid flows are difficult to model within a traditional sharp interface theory. Diffuse interface models turn out to be an attractive alternative to model two-phase flows. Based on a Cahn{Hilliard{Navier{Stokes model introduced by Abels, Garcke and Gr un (Math. Models Methods Appl. Sci. 2012), which uses a volume averaged velocity, we derive a diffuse interface model in a Hele{ Shaw geometry, which in the case of non-matched densities, simplifies an earlier model of Lee, Lowengrub and Goodman (Phys. Fluids 2002). We recover the classical Hele{ Shaw model as a sharp interface limit of the diffuse interface model. Furthermore, we show the existence of weak solutions and present several numerical computations including situations with rising bubbles and fingering instabilities.Hele-Shaw flowsmulti-phase flowsCahn-Hilliard modeldiffuse interfacessharp interface limitisogeometric analysistext::working paper