Calculation of the horizontal two-dimensional unsteady flows by the method of characteristics

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

Aloev

Bliyeva

Dadabayev

et al. 2022

Symmetry

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Calculation of the horizontal two-dimensional unsteady flows by the method of characteristics

Abstract: This paper will be concerned with the characteristic form of the two dimensional Saint-Venant equation system, the supplementary equations at the boundaries, the methods of characteristics for solving the equation system and some numerical experiments.

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

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

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