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A hybrid level set / front tracking approach

In finite element simulations of fluid flows with free boundaries, the representation of boundaries and interfaces plays an essential role. Common approaches can be categorized into two groups, interface tracking and interface capturing methods, each with individual pros and cons. The proposed approach provides a hybrid description of the interface. The main ingredient is a mesh optimization technique that aligns a given triangulation to the geometry which is implicitly represented by a level set function. Resulting triangulations are of optimal quality while connectivity of the mesh is retained. Consequently, finite element spaces defined on the aligned triangulations can be efficiently modified to account for solution specific properties such as discontinuities across interfaces.