Geodesic
Numerical modeling of some self-similar flows of perfect gas
Matematičeskoe modelirovanie, Tome 10 (1998) no. 6, pp. 31-41.

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This paper is devoted to detailed numerical investigation of similar solutions of “piston problem” and Cauchy problem for one-dimentional plane non-stationary gasdynamic equations as well as to studing of solutions existence and their space-time properties demonstration. Earlier studying of these solutions was accomplished by analytical methods. Here quantitative conditions of similar regimes realization under violation of exact (similar) boundary conditions are determined by numerical modelling. Stability of solutions are studied and criterions of their convergence to similar behavior are obtained. 
@article{MM_1998_10_6_a2,
     author = {A. P. Mikhailov and A. A. Shamray},
     title = {Numerical modeling of some self-similar flows of perfect gas},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {31--41},
     publisher = {mathdoc},
     volume = {10},
     number = {6},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_1998_10_6_a2/}
}
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A. P. Mikhailov; A. A. Shamray. Numerical modeling of some self-similar flows of perfect gas. Matematičeskoe modelirovanie, Tome 10 (1998) no. 6, pp. 31-41. http://geodesic.mathdoc.fr/item/MM_1998_10_6_a2/