SUMMARYSimulating transient compressible ows involving shock waves presents challenges to the CFD practitioner in terms of the mesh quality required to resolve discontinuities and prevent smearing. This paper discusses a novel two-dimensional Cartesian anisotropic mesh adaptation technique implemented for transient compressible ow. This technique, originally developed for laminar incompressible ow, is e cient because it reÿnes and coarsens cells using criteria that consider the solution in each of the cardinal directions separately. In this paper, the method will be applied to compressible ow. The procedure shows promise in its ability to deliver good quality solutions while achieving computational savings.Transient shock wave di raction over a backward step and shock re ection over a forward step are considered as test cases because they demonstrate that the quality of the solution can be maintained as the mesh is reÿned and coarsened in time. The data structure is explained in relation to the computational mesh, and the object-oriented design and implementation of the code is presented. Reÿnement and coarsening algorithms are outlined. Computational savings over uniform and isotropic mesh approaches are shown to be signiÿcant.