The ``asymptotic layering'' method

In a series of papers, Clarke and his collaborators ([1], [3] and references therein), assumed that the shock can be represented by several sublayers of the precursor and wake regions in which the nonequilibrium collisional and radiative ionization processes are locally uncoupled. This assumption permits some appreciable simplifications in the calculation of the shock structure with respect to the fully numerical approach. The used atomic model (hydrogen, helium or argon), which was limited by two bound levels plus a continuum, does not give the possibility to treat relatively complex and realistic absorption spectrum such as in Fig.. Moreover, they employed the formal solution of the transfer equation with iteration procedure to obtain the self-consistent shock wave structure. Consequently, as in the previous approach, the problem of exponential factors was still present when the formal solution is applied for optically thick layers. This attempt to obtain the self-consistent solution for the whole shock wave structure, mainly in shock tube experiments, is certainly the best among known in the litterature.