NUMERICAL SOLUTION OF A MIXED PROBLEM FOR A TWO-DIMENSIONAL SYSTEM OF SAINT-VENANT EQUATIONS - Berdyshev, A.; Aloev, R.; Akbarova, A.; Abdiramanov, Zh. (Bulletin of Abai KazNPU. Series of Physical and Mathematical sciences, 2022)
The work is devoted to the construction and study of a numerical method for solving the Saint-Venant equation. These equations are of great practical importance in modern hydraulic engineering and are suitable for describing natural processes in the atmosphere, rivers, and oceans, as well as for modeling tides. Questions of formulation of mixed problems for the two-dimensional system of Saint-Venant equations, are studied. A new upwind difference scheme of splitting in spatial directions is constructed for solving the mixed problem of the two-dimensional Saint-Venant equation, which describes flows without turbulent diffusion components. The stability of the difference scheme concerning energy norms is established. The results of numerical experiments for model problems are presented, including a numerical simulation of water flow in the Ugam River. The numerical calculation is based on the use of the two-point sweep method.