An Introduction to front Tracking

In fluid flows one can often identify surfaces that correspond to special features of the flow. Examples are boundaries between different phases of a fluid or between two different fluids, slip surfaces, and shock waves in compressible gas dynamics. These prominent features of fluid dynamics present formidable challenges to numerical simulations of their mathematical models. The essentially nonlinear nature of these waves calls for nonlinear methods. Here we present one such method which attempts to explicitly follow (track) the dynamic evolution of these waves (fronts). Most of this exposition will concentrate on one particular implementation of such a front tracking algorithm for two space, where the fronts are one-dimensional curves. This is the code associated with J. Glimm and many co-workers.