Geodesic
Mathematical modeling of shock-wave processes under gas solid boundary interaction
Informatics and Automation, Modern problems of mechanics, Tome 281 (2013), pp. 42-54.

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The results of numerical simulations are presented for planar air flows in a bounded volume of square cross section diminishing due to a uniform motion of the walls, for a flow of a propane–air mixture under sinusoidal variation of the size of the square domain, and for three-dimensional supersonic air and propane–air flows in channels of variable square cross section. Specific features of shock-wave processes that are associated with the piston effect and cumulation are established. The hypersonic analogy between planar and spatial flows is confirmed, which allows one to use two-dimensional solutions in estimating three-dimensional flows. The equations of a multicomponent ideal perfect gas and one-stage kinetics of chemical reactions are used to describe the flows. The method of numerical simulations is based on S. K. Godunov's scheme and implemented within an original software package. 
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V. A. Levin; I. S. Manuylovich; V. V. Markov. Mathematical modeling of shock-wave processes under gas solid boundary interaction. Informatics and Automation, Modern problems of mechanics, Tome 281 (2013), pp. 42-54. http://geodesic.mathdoc.fr/item/TRSPY_2013_281_a4/

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