Shock tracking methods in 2D flows

It is pointed out that a wide range of physical systems involve regions of smoothly varying physical properties separated by sharp transition zones or discontinuities. When applied to such systems, standard numerical methods often fail, because of the lack of smoothness near discontinuities. A description is provided of methods which have been developed for solving such problems. In the development of these methods, it has been assumed that the location of the discontinuity curves is known. A generalized planar interface is defined as a set of nodes joined by nonintersecting directed curves. Attention is given to elliptic, parabolic and hyperbolic problems.