International Conference «Mathematical and Informational Technologies, MIT-2013»

(X Conference «Computational and Informational Technologies for Science,

Engineering and Education»)

## Kovyrkina O.A. Ostapenko V.V.## Theoretical and numerical modelling of wave liquid flows in the non-prismatic channel## Reporter: Kovyrkina O.A.In the first approximation of one-dimensional shallow water theory, theoretical and numerical modelling of wave liquid flows in the non-prismatic channel is investigated. In this case the dam break problem on the cross section jump in rectangular channel is considered. The unique solvability of the problem is proved in case if the width of the channel in the upper pool is greater then in the lower pool. We assume that the energy relation on the cross section jump is fulfilled. It includes the heuristic parameter setting the part of the total energy of a stream which remains at a transition through the jump is executed. The concrete value of the parameter is chosen by the comparison of one-dimensional solutions with the results of numerical modelling of this problem on the base of the two-dimensional shallow water equations. The comparison of the exact self-similar solutions and the results of two-dimensional numerical simulation on possible types of waves, their spreading velocities and depth beyond their fronts is conducted.
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