Differential EquationsDifferential Equations0374-06413034-5030Russian Academy of Science10.31857/S0374064123070117Setochno-kharakteristicheskiy metod povyshennogo poryadka dlya sistem giperbolicheskikh uravneniy s kusochno-postoyannymi koeffitsientamiСеточно-характеристический метод повышенного порядка для систем гиперболических уравнений с кусочно-постоянными коэффициентамиKhokhlovN. IХохловН. И khokhlov.ni@mipt.ruPetrovI. BПетровИ. Б petrov@mipt.ruМосковский физико-технический институт (национальный исследовательский университет)Moscow Institute of Physics and TechnologyМосковский физико-технический институт (национальный исследовательский университет)Moscow Institute of Physics and Technology15072023597983995

A new approach is considered for increasing the order of accuracy of the grid-characteristic method in the region of coefficient jumps. The approach is based on piecewise polynomial interpolation for schemes of the second and third orders of accuracy for the case where the interface between the media is consistent with a finite-difference grid. The method is intended for numerical simulation of the propagation of dynamic wave disturbances in heterogeneous media. Systems of hyperbolic equations with variable coefficients are used to describe the considered physical processes. The description of the numerical method and the results of its testing are given.

Рассмотрен новый подход для повышения порядка точности сеточно-характеристического метода в области скачка коэффициентов, основанный на кусочно-полиномиальной интерполяции для схем второго и третьего порядков точности, для случая, когда граница раздела сред согласована с конечно-разностной сеткой. Метод предназначен для численного моделирования распространения динамических волновых возмущений в гетерогенных средах. Для описания рассматриваемых физических процессов использованы системы гиперболических уравнений с переменными коэффициентами. Приведены описание численного метода и результаты его тестирования.

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