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Weak steady Mach reflections are numerically simulated using unstructured grids by means of either "shock-fitting" or "shock-capturing" techniques. It is shown that shock-fitting allows using coarser meshes than those required by shock-capturing, since the latter needs mesh refinement in the direction normal to the discontinuities, which is not needed using the former approach. The shock-fitted solution is also free from the numerical disturbances that arise along the captured discontinuities and pollute the captured solution in the smooth flowfield region. Finally, the shock-fitting solutions show the presence of a small region next to the Mach stem and the reflected shock downstream of the triple point, characterized by very high gradients

An unstructured, shock-fitting algorithm, originally developed to simulate steady flows, has being further developed to make it capable of dealing with unsteady flows. The present paper discusses and analyses the additional features required to extend to unsteady flows, the steady algorithm. The properties of the unsteady version of this novel, unstructured shock-fitting technique, are tested by reference to the inviscid interaction between a vortex and a planar shock: a comparative assessment of shock-capturing and shock-fitting is made for the same test problem