A variational method for multiphase area-preserving interface motions

TL;DR

This paper introduces a novel vector-based thresholding algorithm for simulating multiphase mean curvature flow that preserves phase areas, addressing grid inaccuracy issues and validated through analysis and numerical tests.

Contribution

It extends the Bence-Merriman-Osher algorithm to multiphase area-preserving motions with a new correction method for grid inaccuracies.

Findings

Effective preservation of phase areas during simulations

Improved accuracy on non-adaptive grids

Validated through formal analysis and numerical experiments

Abstract

We develop a numerical method for realizing mean curvature motion of interfaces separating multiple phases, whose areas are preserved throughout time. The foundation of the method is a thresholding algorithm of the Bence-Merriman-Osher type. The original algorithm is reformulated in a vector setting, which allows for a natural inclusion of constraints, even in the multiphase case. Moreover, a new method for overcoming the inaccuracy of thresholding methods on non-adaptive grids is designed, since this inaccuracy becomes especially prominent in area-preserving motions. Formal analysis of the method and numerical tests are presented.