Geodesic
Exact solutions of shallow water equations for the water oscillation problem in a simulated basin and their implementation in verifying numerical algorithms
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 22 (2019) no. 3, pp. 281-299.

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We present the approaches to solving a problem of shallow water oscillations in a parabolic basin (including an extra case of a horizontal plane). A series of assumptions about the form of solution and effects of Earth‘s rotation and bottom friction are made. Then the resulting ODE systems are solved. The corresponding free surfaces have first or second order. The conditions of finiteness and localization of a flow are analyzed. The solutions are used in the verification of numerical algorithm of the large particles method, the efficiency of the carried out tests is discussed. 
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N. A. Matskevich; L. B. Chubarov. Exact solutions of shallow water equations for the water oscillation problem in a simulated basin and their implementation in verifying numerical algorithms. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 22 (2019) no. 3, pp. 281-299. http://geodesic.mathdoc.fr/item/SJVM_2019_22_3_a2/

[1] Ball F. K., “An exact theory of simple finite shallow water oscillations of a rotating Earth”, Proc. of the First Australian Conference on Hydraulics and Fluid Mechanics, Pergamon, 1964, 293–305 | DOI

[2] Bi S., Zhou J., Liu Y., Song L., “A finite volume method for modeling shallow flows with wet-dry fronts on adaptive cartesian grids”, Mathematical Problems in Engineering, 2014 (2014), 209562, 20 pp. | MR | Zbl

[3] Carrier G. F., Greenspan H. P., “Water waves of finite amplitude on a sloping beach”, J. of Fluid Mechanics, 4:4 (1958), 97–109 | DOI | MR | Zbl

[4] Didenkulova I., Pelinovsky E., “Run-up of tsunami waves in U-shaped bays”, Pure and Applied Geophysics, 168:6–7 (2011), 1239–1249 | DOI

[5] Kesserwani G., Liang O., “Locally limited and fully conserved RKDG2 shallow water solutions with wetting and drying”, J. of Scientific Computing, 50:1 (2012), 120–144 | DOI | MR | Zbl

[6] Rybkin A., Pelinovsky E., Didenkulova I., “Nonlinear wave run-up in bays of arbitrary cross-section: generalization of the Carrier-Greenspan approach”, J. of Fluid Mechanics, 748 (2014), 416–432 | DOI | MR

[7] Sampson J. A., “A numerical solution for moving boundary shallow water flow above parabolic bottom topography”, J. of Australia and New Zealand Industrial and Applied Mathematics, 50 (2009), C898–C911 | MR

[8] Sielecki A., Wurtele M. G., “The numerical integration of the nonlinear shallow-water equations with sloping boundaries”, J. of Computational Physics, 6:2 (1970), 219–236 | DOI | Zbl

[9] Spielvogel L. Q., “Single-wave run-up on sloping beaches”, J. of Fluid Mechanics, 74:4 (1975), 685–694 | DOI

[10] Synolakis C. E., “The runup of solitary waves”, J. of Fluid Mechanics, 185 (1987), 523–545 | DOI | Zbl

[11] Thacker W. C., “Some exact solutions to the nonlinear shallow-water wave equations”, J. of Fluid Mechanics, 107 (1981), 499–508 | DOI | MR | Zbl

[12] Belotserkovskii O. M., Davydov Yu. M., Metod krupnykh chastits v gazovoi dinamike, Nauka, Glavnaya redaktsiya fiziko-matematicheskoi literatury, M., 1982

[13] Marchuk A. G., Chubarov L. B., Shokin Yu. I., Chislennoe modelirovanie voln tsunami, Nauka, Sibirskoe otdelenie, Novosibirsk, 1983

[14] Shokin Yu. I., Beizel' S. A., Rychkov A. D., Chubarov L. B., “Chislennoe modelirovanie nakata voln tsunami na poberezh'e s ispol'zovaniem metoda krupnykh chastits”, Matematicheskoe modelirovanie, 27:1 (2015), 99–112 | Zbl