Geodesic
Numerical model for the shallow water equations on a curvilinear grid with the preservation of the Bernoulli integral
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 7, pp. 1317-1324

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Methodological aspects concerning the construction of a two-dimensional numerical model for reservoir flows based on the shallow water equations are considered. A numerical scheme is constructed by applying the control volume method on staggered grids in combination with the Bernoulli integral, which is used to interpolate the desired fields inside a grid cell. The implementation of the method yields a monotone numerical scheme. The results of numerical integration are compared with the exact solution. 
@article{ZVMMF_2012_52_7_a13,
     author = {V. A. Shlychkov},
     title = {Numerical model for the shallow water equations on a curvilinear grid with the preservation of the {Bernoulli} integral},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1317--1324},
     publisher = {mathdoc},
     volume = {52},
     number = {7},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_7_a13/}
}
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V. A. Shlychkov. Numerical model for the shallow water equations on a curvilinear grid with the preservation of the Bernoulli integral. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 7, pp. 1317-1324. http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_7_a13/