Geodesic
A numerical scheme for simulating the dynamics of surface water
Numerical methods and programming, Tome 12 (2011) no. 2, pp. 282-297

Voir la notice de l'article provenant de la source Math-Net.Ru

A new numerical algorithm is developed for calculating the shallow water dynamics. The algorithm provides a cross-cutting computation on irregular or/and discontinuous reliefs with unsteady boundaries of the “water-dry bottom” type. The method is based on the combination of modified SPH and TVD approaches for the shallow water equations. A large number of classical problems is tested. The numerical results show that the combined SPH-TVD scheme is conservative, well-balanced, has the second order of accuracy on smooth solutions. This scheme has the first order of accuracy in the domains containing discontinuities of the flow parameters and kinks of the relief profile.
Keywords: shallow water equations; numerical scheme; SPH; TVD; irregular bottom topography. 
@article{VMP_2011_12_2_a8,
     author = {S. S. Khrapov and A. V. Khoperskov and N. M. Kuz'min and A. V. Pisarev and I. A. Kobelev},
     title = {A numerical scheme for simulating the dynamics of surface water},
     journal = {Numerical methods and programming},
     pages = {282--297},
     publisher = {mathdoc},
     volume = {12},
     number = {2},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2011_12_2_a8/}
}
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S. S. Khrapov; A. V. Khoperskov; N. M. Kuz'min; A. V. Pisarev; I. A. Kobelev. A numerical scheme for simulating the dynamics of surface water. Numerical methods and programming, Tome 12 (2011) no. 2, pp. 282-297. http://geodesic.mathdoc.fr/item/VMP_2011_12_2_a8/