New Mass-Conserving Algorithm for Level Set Redistancing on Unstructured Meshes

The level set method is becoming increasingly popular for the simulation of several problems that involve interfaces. The level set function is advected by some velocity field, with the zero-level set of the function defining the position of the interface. The advection distorts the initial shape of the level set function, which needs to be re-initialized to a smooth function preserving the position of the zero-level set. Many algorithms re-initialize the level set function to (some approximation of) the signed distance from the interface. Efficient algorithms for level set redistancing on Cartesian meshes have become available over the last years, but unstructured meshes have received little attention. This presentation concerns algorithms for construction of a distance function from the zero-level set, in such a way that mass is conserved on arbitrary unstructured meshes. The algorithm is consistent with the hyperbolic character of the distance equation $(‖∇d‖=1)$ and can be localized on a narrow band close to the interface, saving computing effort. The mass-correction step is weighted according to local mass differences, an improvement over usual global rebalancing techniques.