Publication:
On one approach for the numerical solving of hyperbolic initial-boundary problems on an adaptive moving grids

Дата
2023
Авторы
Shilnikov, K. E.
Kochanov, M. B.
Journal Title
Journal ISSN
Volume Title
Издатель
Научные группы
Организационные подразделения
OrgUnit Logo
Организационная единица
Институт лазерных и плазменных технологий
Стратегическая цель Института ЛаПлаз – стать ведущей научной школой и ядром развития инноваций по лазерным, плазменным, радиационным и ускорительным технологиям, с уникальными образовательными программами, востребованными на российском и мировом рынке образовательных услуг.
Выпуск журнала
Аннотация
An approach for the quality improvement of numerical modeling of the processes described by nonlinear hyperbolic equations, which have conservative form is proposed. The transition to synchronous moving coordinate system along with Godunov type numerical scheme for the problem on moving mesh is applied. The grid motion law relies heavily on Rankine–Hugoniot relations. In order to prevent the degeneration of moving computational mesh the regularization mechanism is implemented. It allows to almost automatically fit the computational mesh to the admissible width of the solution singularity resolution. The proposed algorithm is tested on several initial-boundary problems for the Hopf equation with well known exact solutions. The hyperbolic Buckley–Leverett equation is also considered as an example of application of the proposed approach. © 2022 Elsevier B.V.
Описание
Ключевые слова
Dynamic adaptation , Nonlinear partial differential equations , Numerical methods , Singular solutions
Цитирование
Shilnikov, K. E. On one approach for the numerical solving of hyperbolic initial-boundary problems on an adaptive moving grids / Shilnikov, K.E., Kochanov, M.B. // Journal of Computational and Applied Mathematics. - 2023. - 421. - 10.1016/j.cam.2022.114884
URI
https://www.doi.org/10.1016/j.cam.2022.114884
 https://www.scopus.com/record/display.uri?eid=2-s2.0-85140307134&origin=resultslist
 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=Alerting&SrcApp=Alerting&DestApp=WOS_CPL&DestLinkType=FullRecord&UT=WOS:000877609900012
 https://openrepository.mephi.ru/handle/123456789/29859
Коллекции
Публикации