A New Level-Set Model for the Representation of Non-Smooth Geometries

In Starinshak et al. (J Comput Phys 262(1):1–16, 2014), we proposed a new level-set model for representing multimaterial flows in multiple space dimensions. Rather than associating each level-set function with the boundary of a material, the new model associates each level-set function with a pair of materials and the interface that separates them. In this paper, we extend the model to represent geometries with non-smooth boundaries. The model uses multiple level-set functions to describe the shape boundary, typically with one level-set function per smooth boundary segment. Sign information is collected from all level-set functions and a voting algorithm is used to determine the interior/exterior of the geometric shape. The model is well suited for representing boundaries with singularities; it offers significant improvement over standard level-set approaches, both in shape preservation and area conservation; and it eliminates the need for costly redistancing of the level-set function. Numerical examples illustrate the superior performance of the proposed model.