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  4. T. 63, № 10, 2023

Журнал вычислительной математики и математической физики, 2023, T. 63, № 10, стр. 1687-1705

Исследование сеточной сходимости сеточно-характеристического метода на химерных сетках в задаче ультразвукового неразрушающего контроля рельсового полотна

А. А. Кожемяченко 1, 2, *, А. В. Фаворская 1, 2

1 Московский физико-технический институт
141701 М.о., Долгопрудный, Институтский пер., 9, Россия

2 Научно-исследовательский институт системных исследований РАН
117218 Москва, Нахимовский пр-т., 36, к. 1, Россия

* E-mail: anton-kozhemyachenko@yandex.ru

Поступила в редакцию 27.05.2023
После доработки 27.05.2023
Принята к публикации 26.06.2023

Аннотация

В работе рассматривается пример решения трехмерной прямой задачи ультразвукового контроля в рельсовом полотне, представляемого в виде линейно-упругой среды, с использованием сеточно-характеристического метода на криволинейной структурированной химерной и регулярных структурированных сетках. Между химерной и регулярными сетками используется взаимная интерполяция, учитывающая особенности перехода от криволинейной к регулярной сеткам в трехмерном пространстве. Предложен аналитический алгоритм для построения химерной сетки. Приведены анализ сходимости разработанных численных алгоритмов в зависимости от изменения шага по пространственным направлениям и сравнительный анализ полноволновых полей модуля скорости распространения возмущения от источника. Библ. 43. Фиг. 17.

Ключевые слова: численное моделирование, сеточно-характеристический метод, химерные сетки, неразрушающий контроль, ультразвуковой метод, рельсовое полотно.

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