Geodesic
Necessity of entropy control in gasdynamic computations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 9, pp. 1591-1601

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A recently published numerical approach is used to perform an analytical study of the behavior of entropy in the numerical integration of gas dynamics equations. The study confirms the existence of discontinuous solutions for which the principle of nondecreasing entropy can be violated. A simple entropy-controlling algorithm is proposed for gasdynamic flow computations and other numerical methods. 
@article{ZVMMF_2007_47_9_a12,
     author = {G. P. Prokopov},
     title = {Necessity of entropy control in gasdynamic computations},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1591--1601},
     publisher = {mathdoc},
     volume = {47},
     number = {9},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_9_a12/}
}
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G. P. Prokopov. Necessity of entropy control in gasdynamic computations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 9, pp. 1591-1601. http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_9_a12/