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1996, 1999, 2006
J.A. Sethian

Coupling Level Set Methods to Physical Problems You are currently in the topic outlined in red. Click on navigable flow chart to go to new topic click on any text to go to a new topic.

Coupling to General Physics

In order to couple level set methods to most physical applications, one must link the position and motion of the interface to physical effects on one or both sides of the interface. This linking often requires solving relevant partial differential equations on either side of the front, and employs jump boundary conditions at the interface itself. Thus, the position of the front influences the physics, and the physics then prescribes the motion of the interface.

In order to develop a general level set implementation of such problems, we need to make an important observation. The Narrow Band level set methods contains two embeddings. First, the propagating interface is embedded as the zero level set of the higher dimensional level set function. This allows one to track topological changes in the interface, and calculate geometric quantities from the smooth level set function.

Equally important, the speed F of the interface in its normal direction is embedded in this higher dimensional view; an extension speed function F_ext must be defined must be defined in a neighborhood of the zero level set. In other words, we must extend the speed F off of the interface to the neighboring level sets.

The choice of which extension to use is crucial. While tempting to use those given by the underlying physics (such as, for example, the fluid velocity away from the front), this leads to poor results, including the loss of mass and inaccuracy. Remedies to repair these errors through so-called "re-initialization techniques" (that is, stopping the calculation every time step and building a wholly new level set function) are fraught with their own problems; they can change the position of the interface.