A linear, second-order, energy stable, fully adaptive finite-element method for phase-field modeling of wetting phenomena

Aymard, Benjamin; Vaes, Urbain; Pradas, Marc and Kallidasis, Serafim (2019). A linear, second-order, energy stable, fully adaptive finite-element method for phase-field modeling of wetting phenomena. Journal of Computational Physics: X, 2, article no. 100010.

DOI: https://doi.org/10.1016/j.jcpx.2019.100010

Abstract

We propose a new numerical method to solve the Cahn-Hilliard equation coupled with non-linear wetting boundary conditions. We show that the method is mass-conservative and that the discrete solution satisfies a discrete energy law similar to the one satisfied by the exact solution. We perform several tests inspired by realistic situations to verify the accuracy and performance of the method: wetting of a chemically heterogeneous substrate in three dimensions, wetting-driven nucleation in a complex two dimensional domain and three-dimensional diffusion through a porous medium.

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