This research involves a new 3D method for tracking dynamic interfaces that supersedes the state of the art in the simulation of complex fluid phenomena in terms of accuracy and utility. This new 3D method, termed the Marker Level Set (MLS) method, provides an integrated solution to several challenges of the present fluid methodologies. It is accurate, has the ability to easily deal with topology changes in two or three dimensions, has good volume conservation properties, provides interfacial tangential dynamics and is efficient. None of the existing interface tracking methods combine all these qualities in the same formulation. The theories, algorithms, systems and applications derived from this research are useful to both computer graphics and medical applications, as well as to fields related to computational fluid dynamics.
The Marker Level Set method combines the use of level sets and markers placed only along the interface. This is computationally efficient and accurate since the markers provide characteristic surface information. In addition, the MLS method naturally provides tangential surface dynamics, something missing from the other level set based methods. This property is very useful for advecting textures in the fields of graphics and visualization. Finally, MLS allows modeling the interaction of fluids with deformable bodies.
