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Article title THE GRID APPROXIMATIONS AT THE SHALLOW WATER EQUATIONS ON A CURVE-LINEAR MESHES
Authors V.S. Vasiliev
Section SECTION II. MATHEMATICAL MODELING OF AERO- AND HYDROPHYSICS
Month, Year 06, 2010 @en
Index UDC 519.6
DOI
Abstract The conservative and symmetric approximations of a item of divergent of vector are constructed. The approximations of gradient of scalar are constructed to provide conjugation. Conjugation provides positive definition grid operator of the free surface elevation equation. Symmetry provides a base metric identities therefore exclude arising of a grid sources of same types.

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Keywords Mathematical simulation; grid methods; curve-linear meshes; grid approximations; con- servative lows.
References 1. Васильев В.С. Аппроксимации в системах уравнений мелкой воды на криволинейных сетках // Известия ЮФУ. Технические науки. – 2007. – № 2 (77). – С. 135-141.
2. Вольцингер Н.Е., Клеванный К.А., Пелиновский Е.Н. Длинноволновая динамика прибрежной зоны. – Л.: Гидрометеоиздат, 1989. – 271 с.
3. Филатов Н.Н. Гидродинамика озер. – СПб.: Наука, 1991. – 200 с.
4. Agoshkov V.I., Saleri F. Recent Developments in the Numerical Simulation of Shallow Water Equations. III – Boundary Conditions and Finite Element Approximations in the River Flow Calculations // Матем. Моделирование. – 1996. – Т. 8, № 9. – С. 3-24.

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