Exact solutions of shallow water equations for the water oscillation problem in a simulated basin and their implementation in verifying numerical algorithms
N.A. Matckevich1,2, L.B. Chubarov1,2
1Novosibirsk State University, Novosibirsk, Russia
2Institute of Computational Technologies SB RAS, Novosibirsk, Russia
Keywords: накат волн на берег, свободная поверхность, сила Кориолиса, сила донного трения, математическое моделирование, уравнения мелкой воды, аналитические решения, обыкновенные дифференциальные уравнения, численные алгоритмы, метод крупных частиц, верификация, 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
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.
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