Stability Analysis of an Upwind Difference Splitting Scheme for Two-Dimensional Saint–Venant Equations
Berdyshev A. Aloev R. Bliyeva D. Dadabayev S. Baishemirov Z.
October 2022MDPI
Symmetry
2022#14Issue 10
The paper is devoted to the construction and study of a numerical method for solving two-dimensional Saint–Venant equations. These equations have important applied significance in modern hydraulic engineering and are suitable for describing waves in the atmosphere, rivers and oceans, and for modeling tides. The issues of formulation of the mixed problems for these equations are studied. The system of equations is reduced to a symmetrical form by transforming dependent variables. Then, the matrices of coefficients are represented as the sums of two symmetric semidefinite matrices. This transformation allows constructing an upwind difference scheme in spatial directions to determine the numerical solution of the initial boundary value problem. The stability of the proposed difference scheme in energy norms is rigorously proved. The results of numerical experiments conducted for a model problem are provided to confirm the stability of the proposed method.
Saint–Venant equations , splitting scheme , stability , upwind difference scheme
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Department of Mathematics and Mathematical Modelling, Institute of Mathematics, Physics and Informatics, Abai Kazakh National Pedagogical University, Almaty, 050000, Kazakhstan
Institute of Information and Computational Technologies SC MES, Almaty, 050010, Kazakhstan
Department of Computational Mathematics and Information Systems, Faculty of Applied Mathematics and Intellectual Technology, Ulugbek National University of Uzbekistan, Tashkent, 100174, Uzbekistan
Department of Information Technologies, Faculty of Information Technologies and Computer Engineering, Andijan State University, Andijan, 170100, Uzbekistan
School of Applied Mathematics, Kazakh-British Technical University, Almaty, 050000, Kazakhstan
Department of Mathematics and Mathematical Modelling
Institute of Information and Computational Technologies SC MES
Department of Computational Mathematics and Information Systems
Department of Information Technologies
School of Applied Mathematics
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