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Stability Analysis of an Upwind Difference Splitting Scheme for Two-Dimensional Saint–Venant Equations

Abdumauvlen BerdyshevInstitute of Information and Computational Technologies SC MES, Almaty 050010, KazakhstanRakhmatillo AloevDepartment of Computational Mathematics and Information Systems, Faculty of Applied Mathematics and Intellectual Technology, Ulugbek National University of Uzbekistan, Tashkent 100174, UzbekistanDana BliyevaInstitute of Information and Computational Technologies SC MES, Almaty 050010, KazakhstanSardor DadabayevDepartment of Information Technologies, Faculty of Information Technologies and Computer Engineering, Andijan State University, Andijan 170100, UzbekistanZharasbek BaishemirovInstitute of Information and Computational Technologies SC MES, Almaty 050010, Kazakhstan

Symmetryjournal2022en

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ABI

Annotatsiya

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.

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Mavzular

Differential Equations and Numerical Methods Computational Fluid Dynamics and Aerodynamics Numerical methods for differential equations

Identifikatorlar

DOI: 10.3390/sym14101986

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