This article is cited in 10 papers

Exact solutions of shallow water equations for the water oscillation problem in a simulated basin and their implementation in verifying numerical algorithms

N. A. Matskevich^ab, L. B. Chubarov<sup>ba

a</sup> Institute of Computational Technologies, Siberian Branch, Russian Academy of Sciences, pr. Akad. Lavrent’eva 6, Novosibirsk, 630090 Russia
^b Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090 Russia

Abstract: 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.

Key words: wave run-up, free surface, Coriolis force, bottom friction, mathematical modeling, shallow water equations, exact solutions, ordinary differential equations, numerical algorithms, large particles method, verification.

UDC: 51.72, 532.591

Received: 13.08.2018
Revised: 07.11.2018
Accepted: 07.05.2019

DOI: 10.15372/SJNM20190303

 English version: Numerical Analysis and Applications, 2019, 12:3, 234–250

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