Конечно-разностная схема полурасщепления матричных коэффициентов и ее применение для описания распространения цунами

Abstract

Представлены конечно-разностная схема полурасщепления матричных коэффициентов одномерных уравнений газовой динамики и результаты расчетов по одномерному вычислительному коду, составленному на основе этой схемы, для решения задачи о распространении мегацунами в океане и выхода волны на береговую зону океана. Показана пригодность предлагаемого в данной работе вычислительного кода для решения задачи о накате морской волны на сушу. Дальнейшее развитие работы видится в разработке двухмерной программы расчета распространения поверхностной волны. The well-known finite-difference scheme of Moretti of splitting the matrix coefficients of the system of gas dynamics equations involves writing equations in a special form – pressure and internal energy are excluded from the equation using the equations of state for an ideal gas. In this paper the author proposes a modification of Moretti scheme as a finite-difference scheme of semi-splitting of matrix coefficients which do not intend to constitute a system of equations in a special form. The semi-splitting scheme allows solving equations of hyperbolic equations of state of any type, for example, even those in tabular form. For one-dimensional equations of propagation of circular wave on the water surface, that are the equations of hyperbolic type, the results of the calculations of the problem of the propagation of a surface wave in the ocean and the output of wave on the shore of the ocean area are given according to one-dimensional computational code of the shallow water theory. Verification of semi-splitting finitedifference scheme is performed by comparing the calculation results for the problem of the propagation of a single surface wave in the ocean and the problem of propagation of a wave train on the ocean surface with the results of calculations of the same problems cited in the work by C. Mader. To calculate the wave setup on the shore the approach is used in the computational code of the shallow water theory, which is described in the work by An. G. Marchuk, A.A. Anisimov. By comparing the calculation results with analytical solutions, the suitability of the computational code proposed in this work for the problem solution of the sea wave setup on land is demonstrated. Further development work is seen in the development of a two-dimensional program for calculating the surface wave propagation.