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On the convergence of a vortical numerical method for three-dimensional Euler equations in Lagrangian coordinates Авторстатья
Информация о цитировании статьи получена из
Web of Science,
Scopus
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 23 декабря 2016 г.
- Авторы: Kiryakin V.Yu, Setukha A.V.
- Журнал: Differential Equations
- Том: 43
- Номер: 9
- Год издания: 2007
- Издательство: Pleiades Publishing, Inc.
- Местоположение издательства: New York, USA
- Первая страница: 1295
- Последняя страница: 1310
- DOI: 10.1134/S0012266107090133
- Аннотация: In the present paper, we investigate the problems of regularization and numerical solution of a three-dimensional vorticity transport equation for an ideal incompressible fluid in Lagrangian coordinates (the Euler equation in the vortex–velocity variables). In the present paper, we first perform the regularization of the vorticity transport equations by smoothing the singularity in the integral representation of the velocity fields via the vorticity according to the Biot–Savart law. Under the assumption of the existence of a smooth solution of original equations on some finite time interval, we prove the solvability of the smoothed equations on the same time interval and the convergence of their solutions to the solutions of the original equations. In addition, the velocity field is considered in the space of functions that have H¨older continuous first derivatives. We perform discretization of the smoothed equations and prove the convergence of the approximate velocity and vorticity fields on a grid in the uniform metric.
- Добавил в систему: Сетуха Алексей Викторович