Geodesic
A modification of Godunov's scheme with Euler variables
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 23 (1983) no. 5, pp. 1240-1244

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An explicit conservative scheme with a rather better stability condition than in the familiar scheme is considered for the equations of gasdynamics. A strong shock wave can be computed without distorting its profile. Computational results for other one-dimensional test problems are also quoted. 
@article{ZVMMF_1983_23_5_a22,
     author = {A. A. Charakhch'yan},
     title = {A modification of {Godunov's} scheme with {Euler} variables},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1240--1244},
     publisher = {mathdoc},
     volume = {23},
     number = {5},
     year = {1983},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_1983_23_5_a22/}
}
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A. A. Charakhch'yan. A modification of Godunov's scheme with Euler variables. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 23 (1983) no. 5, pp. 1240-1244. http://geodesic.mathdoc.fr/item/ZVMMF_1983_23_5_a22/