Treatments of the singularity in the level set method for unstructured meshes

Straightforward computation of normal vectors and curvature of interface is a main advantage of the level set method. However, the level set method may have discontinuities (kinks) in its derivatives that may lead to erroneous estimation of the normal vector and curvature during topological changes. In this study, we extended two existing methods of singularity treatment for the level set method on structured mesh, i.e., the Salac and Lu method (SLM) and local level set extraction method (LOLEX), to those with unstructured mesh in the framework of finite element formulation. An iterative treatment for the dependent nodes that belong to two elements cut by different interfaces was newly proposed for the LOLEX approach on unstructured mesh. Three static simulations showed that the present SLM or LOLEX for unstructured mesh accurately computed the normal vector and the curvature in the regions with singularity. Two dynamic cases were further simulated to investigate the effect of singularity-treatment on the mass conservation as well as the merging mechanism of droplets. While SLM and LOLEX provided results consistent with existing experimental results, it was confirmed that LOLEX provided a better mass conservation and more accurate curvature fields than SLM after coalescence.