Study of shallow water flows over an arbitrary bed profile in the presence of external force

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.