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An extensive series of numerical calculations of oblique shock wave reflections in air and argon have been performed using a version of the second order Eulerian Godunov scheme for inviscid compressible flow. This scheme is among the best of the upwind schemes developed in recent years. The results have been compared with the best available interferometric data from the UTIAS 10 cm x 18 cm shock tube, for fifteen different cases. The objective of this portion of the study was to assess the accuracy of the computer code in computing two-dimensional shocked flow of an inviscid perfect gas. A significant portion of our analysis is devoted to the question of the extent of influence of viscous and vibrational nonequilibrium effects on the experimental flow flieds. Further parametrized series of calculations were performed in an effort to study the feasibility of numerically constructing inviscid transition lines in the (M, theta)-plane. Good agreement with analytic predictions was found for low values of M and, as might be expected, there are substantial discrepancies for M = 8.75. The possibility of using such numerical results in the formulation of accurate transition criteria is discussed. Overall, the computer code has been found to represent a significant predictive capability. The future extension of the code to permit the detailed modelling of nonequilibrium and viscous effects is, however, an important objective.