Motion of Curves in Three Spatial Dimensions Using a Level Set Approach

The level set method was originally designed for problems dealing with codimension one objects, where it has been extremely succesful, especially when topological changes in the interface, i.e., merging and breaking, occur. Attempts have been made to modify it to handle objects of higher codimension, such as vortex filaments, while preserving the merging and breaking property. We present numerical simulations of a level set based method for moving curves in R3, the model problem for higher codimension, that allows for topological changes. A vector valued level set function is used with the zero level set representing the curve. Our results show that this method can handle many types of curves moving under all types of geometrically based flows while automatically enforcing merging and breaking.