Approximation of surface diffusion flow: a second order variational Cahn--Hilliard model with degenerate mobilities

TL;DR

This paper presents a new second order variational Cahn--Hilliard model with degenerate mobilities for approximating surface diffusion flow, along with efficient numerical schemes and experiments demonstrating its advantages.

Contribution

Introduction of a novel second order variational phase field model with degenerate mobilities for better approximation of surface diffusion flow.

Findings

The model achieves a higher order of approximation of the sharp limit.

Numerical schemes effectively simulate surface diffusion flow in 2D and 3D.

Experiments show improved performance over existing Cahn--Hilliard models.

Abstract

This paper tackles the approximation of surface diffusion flow using a Cahn--Hilliard-type model. We introduce and analyze a new second order variational phase field model which associates the classical Cahn--Hilliard energy with two degenerate mobilities. This association allows to gain an order of approximation of the sharp limit. In a second part, we propose some simple and efficient numerical schemes to approximate the solutions, and we provide numerical 2D and 3D experiments that illustrate the interest of our model in comparison with other Cahn--Hilliard models.