Abstract
Analysis of the existing methods and tools for predictive modeling of hydrodynamics suggests the need to develop discrete analogs of the constructed models that have the properties of conservatism, stability and convergence, as well as algorithms for their solution, providing an increase in the accuracy of predictive modeling. In this work, a continuous three-dimensional mathematical model of the hydrodynamics of shallow water bodies is considered, and its discretization is carried out. To solve the problem of hydrodynamics, the method of correction to pressure in the case of variable density was used. When constructing discrete mathematical models of hydrodynamics, the filling of the control cells was taken into account, which made it possible to increase the real accuracy of the solution in the case of a complex geometry of the investigated area by improving the approximation of the boundary. The preservation of the flow at the discrete level of the developed hydrodynamic model, as well as the absence of non-conservative dissipative terms obtained as a result of the discretization of the system of equations, is proved.
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