Median Filters for Anisotropic Wetting / Dewetting Problems

TL;DR

This paper introduces vectorial median filter level set methods for simulating anisotropic multiphase wetting and dewetting, accurately capturing junction conditions and topological changes in complex networks.

Contribution

The paper develops novel median filter-based level set schemes that automatically enforce correct junction angles in anisotropic wetting problems, improving accuracy and robustness.

Findings

Numerical convergence confirms correct triple junction angles.

Methods handle topological changes seamlessly.

Accurate enforcement of anisotropic junction conditions.

Abstract

We present new level set methods for multiphase, anisotropic (weighted) motion by mean curvature of networks, focusing on wetting-dewetting problems where one out of three phases is stationary -- a good testbed for checking whether complicated junction conditions are correctly enforced. The new schemes are vectorial median filters: The level set values at the next time step are determined by a sorting procedure performed on the most recent level set values. Detailed numerical convergence studies are presented, showing that the correct angle conditions at triple junctions (which include torque terms due to anisotropy) are indeed indirectly and automatically attained. Other standard benefits of level set methods, such as subgrid accuracy on uniform grids via interpolation and seamless treatment of topological changes, remain intact.