Numerical methods for tracking interfaces

An overview is given of special numerical methods for tracking discontinuous fronts and interfaces. These methods include surface tracking methods based on connected marker points along the interface, volume tracking methods that track the volume occupied by the solution regions bounded by the interfaces, and moving-mesh methods where the underlying mesh is aligned and moved with the interface. The pros and cons of the current methods are discussed and a new method is proposed that overcomes some of the difficulties encountered in approximating equations with multiple interacting interfaces.

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