Landau-Stanyukovich rule and the similarity parameter for converging shocks

The similarity parameter α of a self-similarity problem of the second kind is determined numerically in the course of solving the basic equations. The Landau-Stanyukovich rule gives an approximate value of α close to the true one. This estimate should be refined in further numerical calculations. The determination of the status of the Landau-Stanyukovich rule and the development of this approach make it possible to find the upper and lower bounds for α(γ) for a given adiabatic index γ. The narrowness of the interval between these values makes it possible to find the value of α different from the true one by 0.01–0.02. In this case, the self-similarity problem of the second kind is actually reduced to a self-similarity problem of the first kind in which the value of α follows from the dimension analysis of the key physical parameters of the problem and does not require solving the equations.