Geodesic
Adaptation of Kuropatenko method for calculating shock waves in Euler coordinates
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 14 (2021) no. 1, pp. 91-103

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For the moment, there is no implementation of the well-proven numerical method of Kuropatenko in Eulerian coordinates. Such implementation has a promising capabilities for solving a certain scope of problems. This paper is devoted to adaptation of Kuropatenko method for calculating shock waves using Euler coordinates. The application area of the original method is limited and does not include the simulation of multicomponent and multiphase flows of reacting mixtures in two- and three-dimensional spaces. The result obtained demonstrate the efficiency of the developed modification and show the advantages of the extension of this method into multidimensional algorithms.
Keywords: shock wave, Kuropatenko method, numerical methods, conservation laws. 
@article{VYURU_2021_14_1_a6,
     author = {P. E. Belyaev and I. R. Makeeva and E. E. Pigasov and D. A. Mastyuk},
     title = {Adaptation of {Kuropatenko} method for calculating shock waves in {Euler} coordinates},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
     pages = {91--103},
     publisher = {mathdoc},
     volume = {14},
     number = {1},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURU_2021_14_1_a6/}
}
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P. E. Belyaev; I. R. Makeeva; E. E. Pigasov; D. A. Mastyuk. Adaptation of Kuropatenko method for calculating shock waves in Euler coordinates. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 14 (2021) no. 1, pp. 91-103. http://geodesic.mathdoc.fr/item/VYURU_2021_14_1_a6/