Geodesic
Conservative-characteristic method for solving hyperbolic systems of equations on triangular computational grids
Numerical methods and programming, Tome 23 (2022) no. 4, pp. 365-378.

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This article considers a conservative-characteristic numerical method for solving hyperbolic systems of equations on triangular computational grids. The main steps of the algorithm are described with the example of solving two-dimensional shallow water equations. The method is verified and compared with the methods developed by other authors on the main tests for shallow water equations over a flat bottom.
Keywords: conservative-characteristic methods, CABARET method, computational fluid dynamics, shallow water, triangular computational grids. 
@article{VMP_2022_23_4_a3,
     author = {V. M. Goloviznin and D. Yu. Gorbachev and N. A. Afanasiev},
     title = {Conservative-characteristic method for solving hyperbolic systems of equations on triangular computational grids},
     journal = {Numerical methods and programming},
     pages = {365--378},
     publisher = {mathdoc},
     volume = {23},
     number = {4},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2022_23_4_a3/}
}
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V. M. Goloviznin; D. Yu. Gorbachev; N. A. Afanasiev. Conservative-characteristic method for solving hyperbolic systems of equations on triangular computational grids. Numerical methods and programming, Tome 23 (2022) no. 4, pp. 365-378. http://geodesic.mathdoc.fr/item/VMP_2022_23_4_a3/