Numerical solution of the self-similar reflection of a strong shock wave

The reflection of a strong shock wave from a wedge in a shock tube is considered. This problem is solved by a finite-volume technique using the MacCormack difference scheme. This numerical method is fully conservative, and the self-similar steady state is obtained by expanding the computational volumes along with the propagation of the incident shock. The errors to be expected in the steady state result are discussed. These errors are mainly due to the inconsistency of the scheme across flow field discontinuities, and some typical situations for an oblique shock are treated. It is shown how the numerical method should be applied to minimize the steady state errors.