MODERN SHOCK CAPTURING METHODS FOR CONSERVATION LAWS
In this survey we describe the constructions of modern shock capturing methods for the computation of discontinuous solutions in nonlinear systems of conservation laws. A typical such method consists of three steps: reconstruction, evolution and averaging. We study in detail several reconstruction and evolution strategies. The aim is to provide a global view on the development in this exciting field and to show how these methods may be used to solve problems in fluid dynamics.