Shock capturing schemes for multidimensional flow

Progress made in the development of a genuinely multidimensional finite volume algorithm for problems in inviscid gas dynamics is presented. The approach entails: (1) the reconstruction of flowfield data using a planar wave pattern in which the strengths and orientations of the component waves are derived independently of the mesh geometry; and (2) the development of a flux formula which provides a numerical approximation to the flux at a finite volume cell face during the passage of waves which are in general oblique to the face. Several algorithms are outlined, and the most recent developments are included. The results of several numerical cases are also included.