Note on Landau–Stanyukovich rule and the similarity parameter of converging shock waves

Abstract

Using similarity methods with general physical assumptions and sufficient mathematical relations, researchers can obtain approximate solutions ready for experimental confirmation. Singh et al. claimed to have analyzed the second-kind self-similar motion of converging cylindrical shock waves in magnetogasdynamics. However, we found the dominated equation (11) and relevant equations of Singh et al. [Chin. Phys. Lett. 28(9) (2011) 094701] as well as the dominated equation (12) and relevant equations of Singh et al. [AIAA J. 48(11) (2010) 2523] being not correct. We show the correct mathematical derivations in details. It seems to us corresponding equations as well as illustrations by Singh et al. are of doubt due to above-mentioned issues. Our results imply the similarity exponent [Formula: see text] obtained by Singh et al. will be close to that for the converging spherical shock waves.