Geodesic
A new phase field model for inhomogeneous minimal partitions, and applications to droplets dynamics
Elie Bretin1 ; Simon Masnou2
1Université de Lyon, Villeurbanne, France
2Université Claude Bernard Lyon 1, Villeurbanne, France
Interfaces and free boundaries, Tome 19 (2017) no. 2, pp. 141-182

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We propose and analyze in this paper a new derivation of a phase-field model to approximate inhomogeneous multiphase perimeters. It is based on suitable decompositions of perimeters under some embeddability condition which allows not only an explicit derivation of the model from the surface tensions, but also gives rise to a Γ-convergence result. Moreover, thanks to the nice form of the approximating energy, we can use a simple and robust scheme to simulate its gradient flow. We illustrate the efficiency of our approach with a series of numerical simulations in 2D and 3D, and we address in particular the dynamics of droplets evolving on a fixed solid.
DOI : 10.4171/ifb/379
Classification : 49-XX, 65-XX
Mots-clés : Phase field model, multiphase perimeter, Γ-convergence, droplets, material sciences, image processing

Elie Bretin  1   ; Simon Masnou  2

1 Université de Lyon, Villeurbanne, France
2 Université Claude Bernard Lyon 1, Villeurbanne, France 
Elie Bretin; Simon Masnou. A new phase field model for inhomogeneous minimal partitions, and applications to droplets dynamics. Interfaces and free boundaries, Tome 19 (2017) no. 2, pp. 141-182. doi: 10.4171/ifb/379
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