Computational Methods for Advancing Interfaces

A large number of computational problems and physical phenomena involve the motion of interfaces separating two or more regions. These can include problems in such areas as fluid mechanics, combustion, materials science, meteorology, and computer vision. In these problems, challenging issues often involve interfaces that change topology, form sharp corners and singularities, depend on delicate geometric quantities such as curvature and normal direction, and involve subtle feedback between the physics and chemistry off the interface and the position/motion of the front itself. In this paper, we will explain some of the issues involved in tracking interfaces, focus on a particular set of numerical techniques that arise from an implicit representation of the interface, and provide an overview of some of the applications that are possible with this view. Dedicated to Professor Steve Davis in thanks for having so generously welcomed me into the warm community of those celebrating his birthday and his work. 1 October 9, 2001 13:37 WorldScientific/ws-b8-5x6-0 final ̇sethian ̇paper ̇steve ̇davis ̇conference 2 Computational Methods for Advancing Interfaces 1.1 Characterizations of Moving Interfaces