Geodesic
Balance-characteristic scheme as applied to the shallow water equations over a rough bottom
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 7, pp. 1142-1160

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The CABARET scheme is used for the numerical solution of the one-dimensional shallow water equations over a rough bottom. The scheme involves conservative and flux variables, whose values at a new time level are calculated by applying the characteristic properties of the shallow water equations. The scheme is verified using a series of test and model problems. 
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     author = {V. M. Goloviznin and V. A. Isakov},
     title = {Balance-characteristic scheme as applied to the shallow water equations over a rough bottom},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1142--1160},
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     volume = {57},
     number = {7},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_7_a5/}
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V. M. Goloviznin; V. A. Isakov. Balance-characteristic scheme as applied to the shallow water equations over a rough bottom. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 7, pp. 1142-1160. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_7_a5/