Semi-implicit representation of sharp features with level sets

Abstract

The present contribution enriches the nowadays “classical” level set implicit representation of geometries with topological information in order to correctly represent sharp features. For this, sharp features are classified according to their positions within elements of the level set support. Based on this additional information, sub-elements and interface-mesh used in a finite element context for integration and application of boundary conditions are modified to match exactly to the sharp features. In order to analyze evolving geometries, Boolean operations on these semi-implicit representations are derived so that the minimal additional information to represent correctly the new geometry is stored. This approach has been successfully applied to complex two-dimensional geometries. It computes in a robust way numerous Boolean operations and guarantees the precision and the convergence rate of the numerical simulations.