Publication: Homogeneous Difference Schemes for the Coupled Problems of Hydrodynamics and Elasticity
Дата
2019
Авторы
Tsygvintsev, I. P.
Krukovskiy, A. Y.
Poveshchenko, Y. A.
Gasilov, V. A.
Journal Title
Journal ISSN
Volume Title
Издатель
Аннотация
Finite-di (R) erence approximations of elastic forces on the staggered moving grid were constructed. For the displacement vectors at the irregular grids in which topological and geometrical structures are subjected to minimal reasonable restrictions, with regard to the <overline>nitedi (R) erence schemes of the elasticity theory problems, approximations of the vector analysis operators in plane and cylindrical geometries were constructed. Taking into account the energy balance of the medium, the families of integral consistent approximations of the vector analysis operators, which are su +/- cient for the discrete modeling of these processes considering the space curvature caused by the cylindrical geometry of the system, were built. The schemes, both using a stress tensor in the full form and dividing it into volumetric and deviator components, were studied. This separation is used to construct homogeneous equations that are applicable for solid body and vaporized phase. The linear theory of elasticity was used. The resulting expressions for the elastic forces were presented in the explicit form for two-dimensional degrees at and axisymmetric geometries for a mesh consisting of triangular and quadrangular cells. Generalization of the method for other cases (non-linear strain tensor, non-Hookean relation between strain and stress, full 3D geometry, etc.) can be performed by analogy, but this was not a subject of the current paper. Using the model problem, comparison between di (R) erent temporal discretizations for the obtained ordinary di (R) erential equations system was carried out. In particular, we considered fully implicit approximation, conservative implicit approximation (Crank Nicolson method), and explicit approximation, which is similar to the \leap-frog" method. The analysis of full energy imbalance and calculation costs showed that the latter is more advantageous. The analysis of the e (R) ectiveness of various temporal approximations was performed via numerical experiments.
Описание
Ключевые слова
Цитирование
Homogeneous Difference Schemes for the Coupled Problems of Hydrodynamics and Elasticity / Tsygvintsev, IP [et al.] // Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki. - 2019. - 161. - № 3. - P. 377-392. - 10.26907/2541-7746.2019.3.377-392
URI
https://www.doi.org/10.26907/2541-7746.2019.3.377-392
https://www.scopus.com/record/display.uri?eid=2-s2.0-85077630435&origin=resultslist
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=Alerting&SrcApp=Alerting&DestApp=WOS_CPL&DestLinkType=FullRecord&UT=WOS:000504035100005
https://openrepository.mephi.ru/handle/123456789/19191
https://www.scopus.com/record/display.uri?eid=2-s2.0-85077630435&origin=resultslist
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=Alerting&SrcApp=Alerting&DestApp=WOS_CPL&DestLinkType=FullRecord&UT=WOS:000504035100005
https://openrepository.mephi.ru/handle/123456789/19191