On the Voronoi Implicit Interface Method
For researchers using level set methods for multiphase flow, this work addresses a critical convergence failure and provides a corrected algorithm.
The paper identifies non-convergence of the Voronoi implicit interface method for multiphase curvature motion with unequal surface tensions, and proposes a variant that fixes this issue and extends the method to unequal mobilities.
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.