Curvature calculations for the level-set method
  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. 
Karl Yngve Lerv{\aa}g and {\AA}smund Ervik
physics.flu-dyn physics.comp-ph