@article {FEDELI2017247, title = {Computer simulations of phase field drops on super-hydrophobic surfaces}, journal = {Journal of Computational Physics}, volume = {344}, year = {2017}, pages = {247 - 259}, abstract = {

We present a novel quasi-Newton continuation procedure that efficiently solves the system of nonlinear equations arising from the discretization of a phase field model for wetting phenomena. We perform a comparative numerical analysis that shows the improved speed of convergence gained with respect to other numerical schemes. Moreover, we discuss the conditions that, on a theoretical level, guarantee the convergence of this method. At each iterative step, a suitable continuation procedure develops and passes to the nonlinear solver an accurate initial guess. Discretization performs through cell-centered finite differences. The resulting system of equations is solved on a composite grid that uses dynamic mesh refinement and multi-grid techniques. The final code achieves three-dimensional, realistic computer experiments comparable to those produced in laboratory settings. This code offers not only new insights into the phenomenology of super-hydrophobicity, but also serves as a reliable predictive tool for the study of hydrophobic surfaces.

}, keywords = {Multigrid, Phase field, Quasi-Newton, Super-hydrophobicity}, issn = {0021-9991}, doi = {https://doi.org/10.1016/j.jcp.2017.04.068}, url = {http://www.sciencedirect.com/science/article/pii/S002199911730356X}, author = {Livio Fedeli} }