Residual distribution schemes: Current status and future trends

In this paper, we discuss a new class of schemes, the residual distribution schemes, adapted to compressible flow problems. They can be seen as a link between pure finite element methods such as the streamline diffusion method and the high order upwind method finite volume schemes. In fact they borrow ideas from both classes and this results in very accurate compact schemes. Up to now, they are mainly adapted to triangular type meshes, but can handle steady and unsteady problems. Since the philosophy is quite different form standard schemes, we will provide a full description of the schemes and many numerical illustrations. Some still unsolved issues will also be discussed.