On calculation of hydraulic bore in open channels

In this paper, the review of the results devoted to construction of finite-difference methods of numerical calculation of hydraulic bore (shock) in open channels, arising, in particular, at the dam destruction is presented. The problem of construction of such methods was set up to the scientists of Laboratory of Applied Hydrodynamics of the Institute of Hydrodynamics SB RAS by M. A. Lavrentiev at the beginning of 60th. In the present paper, the solution to this problem obtained for the model of one-layer “shallow water” is considered. At the same time, the questions of conservativity of difference schemes, weak finite-difference approximation of systems of conservation laws, and construction of high accuracy shock capturing difference schemes connected with the problem mentioned above are discussed here.