Geodesic
Study of shallow water flows over an arbitrary bed profile in the presence of external force
Matematičeskoe modelirovanie, Tome 21 (2009) no. 6, pp. 41-58

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The numerical method for studying hydrodynamic flows over an arbitrary bed profile in the presence of external force is proposed in this paper. The arbitrary bed profile is approximated by a piecewise constant function separating it into a finite number of domains with a stepwise boundary. For implementing the mentioned method and to take into account the external force effect the quasi-two-layer model of hydrodynamic flows over a stepwise boundary is used with regard to features of flow near the step. Based on the proposed algorithm, the numerical simulation of various physical phenomena, such as a breakdown of the rectangular fluid column over an inclined plane, the large-scale motion of fluid in the gravitational field in the presence of Coriolis force over an underlying mountain-like surface, is performed. Computations are made for two dimensional dam-break problem on slope and good agreement with laboratory experiments is obtained. 
@article{MM_2009_21_6_a3,
     author = {K. V. Karelsky and A. S. Petrosyan and A. G. Slavin},
     title = {Study of shallow water flows over an arbitrary bed profile in the presence of external force},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {41--58},
     publisher = {mathdoc},
     volume = {21},
     number = {6},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2009_21_6_a3/}
}
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K. V. Karelsky; A. S. Petrosyan; A. G. Slavin. Study of shallow water flows over an arbitrary bed profile in the presence of external force. Matematičeskoe modelirovanie, Tome 21 (2009) no. 6, pp. 41-58. http://geodesic.mathdoc.fr/item/MM_2009_21_6_a3/