Variant of the Tamm and Mott-Smith solution for describing the structure of a gasdynamic shock in a monatomic gas

The bimodal distribution proposed by Tamm to describe the structure of shock waves is refined on the basis of the analytic iteration of the integral kinetic equation. In correcting this distribution, attention is given to errors associated with the setting of boundary conditions at a finite distance from the center of the shock wave, this approach being traditional for numerical studies. A criterion for determining the shock-front thickness is developed on the basis of compressed Banach mappings, which assures the best approximation to the exact solution over a fixed number of iterations. A comparison with experimental data confirms theoretical results on the Mach-number dependence of shock-wave thickness.