Информация о публикации

Просмотр записей
Инд. авторы: Matskevich N.A., Chubarov L.B.
Заглавие: Exact Solutions to Shallow Water Equations for a Water Oscillation Problem in an Idealized Basin and Their Use in Verifying Some Numerical Algorithms
Библ. ссылка: Matskevich N.A., Chubarov L.B. 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. - 2019. - Vol.12. - Iss. 3. - P.234-250. - ISSN 1995-4239. - EISSN 1995-4247.
Внешние системы: DOI: 10.1134/S1995423919030030; РИНЦ: 41636805; SCOPUS: 2-s2.0-85071735364; WoS: 000485274000003;
Реферат: eng: 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.
Ключевые слова: wave run-up; WAVE RUN-UP; verification; large-particle method; numerical algorithms; ordinary differential equations; exact solutions; shallow water equations; mathematical modeling; bottom friction; Coriolis force; free surface;
Издано: 2019
Физ. характеристика: с.234-250
Цитирование: 
1. Ball, F.K., An Exact Theory of Simple Finite Shallow Water Oscillations of a Rotating Earth, Proc. of the First Australian Conf. on Hydraulics and Fluid Mechanics, Pergamon, 1964, pp. 293–305.
2. Bi, S., Zhou, J., Liu, Y., and Song, L., A Finite Volume Method for Modeling Shallow Flows with Wet-Dry Fronts on Adaptive Cartesian Grids, Math. Probl. Engin., 2014, vol. 2014, pp. 1–20; article ID 209562.
3. Carrier, G.F. and Greenspan, H.P., Water Waves of Finite Amplitude on a Sloping Beach, J. Fluid Mech., 1958, vol. 4, no. 4, pp. 97–109.
4. Didenkulova, I. and Pelinovsky, E., Run-Up of Tsunami Waves in U-Shaped Bays, Pure Appl. Geophys., 2011, vol. 168, nos. 6/7, pp. 1239–1249.
5. Kesserwani, G. and Liang, O., Locally Limited and Fully Conserved RKDG2 Shallow Water Solutions with Wetting and Drying, J. Sci. Comput., 2012, vol. 50, no. 1, pp. 120–144.
6. Rybkin, A., Pelinovsky, E., and Didenkulova, I., Nonlinear Wave Run-Up in Bays of Arbitrary Cross Section: Generalization of the Carrier–Greenspan Approach, J. Fluid Mech., 2014, vol. 748, pp. 416–432.
7. Sampson, J.A., A Numerical Solution for Moving Boundary Shallow Water Flow above Parabolic Bottom Topography, J. Australia New Zealand Industr. Appl. Math., 2009, vol. 50, pp. C898–C911.
8. Sielecki, A. and Wurtele, M.G., The Numerical Integration of the Nonlinear Shallow-Water Equations with Sloping Boundaries, J. Comput. Phys., 1970, vol. 6, no. 2, pp. 219–236.
9. Spielvogel, L.Q., Single-Wave Run-Up on Sloping Beaches, J. Fluid Mech., 1975, vol. 74, no. 4, pp. 685–694.
10. Synolakis, C.E., The Runup of Solitary Waves, J. Fluid Mech., 1987, vol. 185, pp. 523–545.
11. Thacker, W.C., Some Exact Solutions to the Nonlinear Shallow-Water Wave Equations, J. Fluid Mech., 1981, vol. 107, pp. 499–508.
12. Belotserkovskii, O.M. and Davydov, Yu.M., Metod krupnykh chastits v gazovoi dinamike (Method of Large Particles in Gas Dynamics), Moscow: Nauka, 1982.
13. Marchuk, A.G., Chubarov, L.B., and Shokin, Yu.I., Chislennoe modelirovanie voln tsunami (Numerical Simulation of Tsunami Waves), Novosibirsk: Nauka, 1983.
14. Shokin, Yu.I., Beisel, S.A., Rychkov, A.D., and Chubarov, L.B., Numerical Simulation of the Tsunami RunUp on the Coast Using the Method of Large Particles, Mat. Model., 2015, vol. 27, no. 1, pp. 99–112.