Tracking of interfaces for fluid flow: Accurate methods for piecewise smooth problems.

A survey of hyperbolic conservation laws is presented, taking into account a front tracking code for hyperbolic systems. Attention is given to approaches of computer modeling, a hyperbolic degree of freedom, the use of a zero diffusion length, the numerical implementation of zero diffusion by special methods, the stable and the unstable regime, and problems related subgrid phenomena. The computational strategy which allows zero numerical diffusion is based on the tracking of the waves. The method of tracking is a hybrid, which uses the characteristic propagation for certain waves (the 'tracked waves') and a finite difference grid for the other waves. The aim of the front tracking code is to provide a general and flexible method for obtaining accurate solutions to problems which are piecewise smooth.