Curvature calculations for the level-set method

TL;DR

This paper addresses the challenge of accurately computing curvature in the level-set method at regions with kinks, proposing improved discretization schemes that outperform standard methods in test cases.

Contribution

It introduces three novel discretization schemes specifically designed to handle discontinuities in the level-set function for better curvature calculation.

Findings

Improved schemes outperform standard discretization in test cases

Better accuracy in regions with kinks in the level-set function

Enhanced curvature computation for complex interface geometries

Abstract

The present work illustrates a difficulty with the level-set method to accurately capture the curvature of interfaces in regions that are of equal distance to two or more interfaces. Such regions are characterized by kinks in the level-set function where the derivative is discontinuous. Thus the standard discretization scheme is not suitable. Three discretization schemes are outlined that are shown to perform better than the standard discretization on two selected test cases.