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- Title
Stability Analysis of an Upwind Difference Splitting Scheme for Two-Dimensional Saint–Venant Equations.
- Authors
Berdyshev, Abdumauvlen; Aloev, Rakhmatillo; Bliyeva, Dana; Dadabayev, Sardor; Baishemirov, Zharasbek
- Abstract
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.
- Subjects
SHALLOW-water equations; NUMERICAL solutions to initial value problems; NUMERICAL solutions to boundary value problems; HYDRAULIC engineering; SYMMETRIC matrices; CAHN-Hilliard-Cook equation
- Publication
Symmetry (20738994), 2022, Vol 14, Issue 10, pN.PAG
- ISSN
2073-8994
- Publication type
Article
- DOI
10.3390/sym14101986