Exact Solutions to Shallow Water Equations for a Water Oscillation Problem in an Idealized Basin and Their Use in Verifying Some Numerical Algorithms

N. A. Matskevich; L. B. Chubarov

doi:10.1134/S1995423919030030

Exact Solutions to Shallow Water Equations for a Water Oscillation Problem in an Idealized Basin and Their Use in Verifying Some Numerical Algorithms

Результат исследования: Научные публикации в периодических изданиях › статья

Аннотация

We present some approaches to solving a problem of shallow water oscillations in a parabolic basin (including an extra case of a horizontal plane). Some requirements on the form of the solutions and effects of Earth’s rotation and bottom friction are made. The resulting solutions are obtained by solving ODE systems. The corresponding free surfaces are first- or second-order ones. Some conditions of finiteness and localization of the flow are analyzed. The solutions are used to verify the numerical algorithm of the large-particle method. The efficiency of the method is discussed in tests on wave run-up on shore structures.

Язык оригинала	английский
Страницы (с-по)	234-250
Число страниц	17
Журнал	Numerical Analysis and Applications
Том	12
Номер выпуска	3
DOI	https://doi.org/10.1134/S1995423919030030
Состояние	Опубликовано - 1 июл 2019

Доступ к документу

10.1134/S1995423919030030

Link to publication in Scopus

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Matskevich, N. A., & Chubarov, L. B. (2019). Exact Solutions to Shallow Water Equations for a Water Oscillation Problem in an Idealized Basin and Their Use in Verifying Some Numerical Algorithms. Numerical Analysis and Applications, 12(3), 234-250. https://doi.org/10.1134/S1995423919030030

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keywords = "bottom friction, Coriolis force, exact solutions, free surface, large-particle method, mathematical modeling, numerical algorithms, ordinary differential equations, shallow water equations, verification, wave run-up",

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Exact Solutions to Shallow Water Equations for a Water Oscillation Problem in an Idealized Basin and Their Use in Verifying Some Numerical Algorithms. / Matskevich, N. A.; Chubarov, L. B.

В: Numerical Analysis and Applications, Том 12, № 3, 01.07.2019, стр. 234-250.

Результат исследования: Научные публикации в периодических изданиях › статья

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N2 - We present some approaches to solving a problem of shallow water oscillations in a parabolic basin (including an extra case of a horizontal plane). Some requirements on the form of the solutions and effects of Earth’s rotation and bottom friction are made. The resulting solutions are obtained by solving ODE systems. The corresponding free surfaces are first- or second-order ones. Some conditions of finiteness and localization of the flow are analyzed. The solutions are used to verify the numerical algorithm of the large-particle method. The efficiency of the method is discussed in tests on wave run-up on shore structures.

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KW - exact solutions

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KW - large-particle method

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KW - ordinary differential equations

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