%0 Journal Article %J Journal of Computational Physics %D 2017 %T Computer simulations of phase field drops on super-hydrophobic surfaces %A Livio Fedeli %K Multigrid %K Phase field %K Quasi-Newton %K Super-hydrophobicity %X

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.

%B Journal of Computational Physics %V 344 %P 247 - 259 %G eng %U http://www.sciencedirect.com/science/article/pii/S002199911730356X %R https://doi.org/10.1016/j.jcp.2017.04.068