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Computer simulation of water flow in networks on the basis of kinematic approximation

A mathematical model describing the motion of water, which takes place under conditions of equilibrium of the forces of resistance and earth's gravity, is constructed, the so-called equations of the kinematic wave. For this model initial-boundary and variational problems are formulated. A regularization scheme of equations is constructed, which allows its application both for Hat surfaces, as well as for surfaces in which the slope gradient changes quickly. The variational problem was solved by the finite element method. The discretization by spatial variables was carried out by dividing the region into triangular finite elements using bilinear basis functions, time discretization was carried out using a one-time recurrent scheme. The model tested at different test cases. For realization of the constructed models developed application software, which allows algorithms of constructed projection schemes to be used for real territories.