On the Voronoi Implicit Interface Method

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.

An efficient diffusion generated motion method for wetting dynamics

“…in the vicinity of the zero level set of ϕ. Therefore (27) implies that θ ≈ θ Y + O(δt). In all, Step 1 of Algorithm 1 leads to a mean curvature flow for the surface of the liquid domain with a contact angle θ ≈ θ Y .…”

“…A disadvantage is that the accuracy of the method is not very good for multi-phase free interface problems with a triple junction. In general, the convergence rate with respect to the time step of the method is of order O(δt) for smooth curves while it is of order O(δt 1/2 ) when there is a triple junction [27]. Some second-order threshold dynamics schemes have been developed for smooth curves in [17,28].…”