Willmore regularized sharp-interface model for strongly anisotropic solid-state dewetting with axisymmetric geometry: modeling and simulation

Abstract

In this work, we consider the three-dimensional solid-state dewetting with strongly anisotropic surface energy, assuming an axisymmetric morphology of the thin film. However, when surface energy exhibits strong anisotropy, certain orientations may be missing from the equilibrium shapes, which will lead to an ill-posed governing equation. By incorporating the Willmore energy, we define a regularized total free energy and rigorously derive a sharp-interface model based on thermodynamic variations. We further develop a numerical scheme for the sharp-interface model that can preserve two important structural properties, including both the volume-conservation and energy-stability laws. We conclude by presenting a series of numerical simulations that illustrate the accuracy and structure-preserving properties. More importantly, extensive numerical simulations clearly demonstrate that our schemes can significantly enhance mesh quality, which is beneficial for long-term computations.