Dede, Luca and Garcke, Harald and Lam, Kei Fong (2018) A Hele-Shaw-Cahn-Hilliard Model for Incompressible Two-Phase Flows with Different Densities. JOURNAL OF MATHEMATICAL FLUID MECHANICS, 20 (2). pp. 531-567. ISSN 1422-6928, 1422-6952
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Topology 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 et al. (Math Models Methods Appl Sci 22(3):1150013. 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 et al. (Phys Fluids 14(2):514-545, 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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | DIFFUSE INTERFACE MODEL; LONG-TIME BEHAVIOR; ISOGEOMETRIC ANALYSIS; WELL-POSEDNESS; TUMOR-GROWTH; SYSTEM; EQUATIONS; CELL; RECONNECTION; SIMULATION; Hole Shaw-flows; multi-phase flows; Cahn-Hilliard model; diffuse interfaces; sharp interface limit; isogeometric analysis |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 09 Mar 2020 10:40 |
| Last Modified: | 09 Mar 2020 10:40 |
| URI: | https://pred.uni-regensburg.de/id/eprint/14443 |
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