On the Voronoi Implicit Interface Method

TL;DR

This paper evaluates the convergence of the Voronoi implicit interface method for multiphase curvature motion, identifies non-convergence issues in certain cases, and proposes a variant that improves convergence and extends applicability.

Contribution

The authors identify convergence issues in the original Voronoi implicit interface method and introduce a modified version that fixes these issues and handles unequal mobilities.

Findings

Original method does not converge in unequal, additive surface tension cases.

The proposed variant maintains the original spirit and achieves convergence.

The new method extends to cases with unequal mobilities.

Abstract

We present careful numerical convergence studies, using parameterized curves to reach very high resolutions in two dimensions, of a level set method for multiphase curvature motion known as the Voronoi implicit interface method. Our tests demonstrate that in the unequal, additive surface tension case, the Voronoi implicit interface method does not converge to the desired limit. We then present a variant that maintains the spirit of the original algorithm, and appears to fix the non-convergence. As a bonus, the new variant extends the Voronoi implicit interface method to unequal mobilities.