Development of a balanced adaptive time-stepping strategy based on an implicit JFNK-DG compressible flow solver
File(s)
Published version
OA Location
Author(s)
Pan, Yu
Yan, Zhen-Guo
Peiro, Joaquim
Sherwin, Spencer J
Type
Journal Article
Abstract
A balanced adaptive time-stepping strategy is implemented in an implicit discontinuous Galerkin solver to guarantee the temporal accuracy of unsteady simulations. A proper relation between the spatial, temporal and iterative errors generated within one time step is constructed. With an estimate of temporal and spatial error using an embedded Runge-Kutta scheme and a higher order spatial discretization, an adaptive time-stepping strategy is proposed based on the idea that the time step should be the maximum without obviously influencing the total error of the discretization. The designed adaptive time-stepping strategy is then tested in various types of problems including isentropic vortex convection, steady-state flow past a flat plate, Taylor-Green vortex and turbulent flow over a circular cylinder at Re=3900. The results indicate that the adaptive time-stepping strategy can maintain that the discretization error is dominated by the spatial error and relatively high efficiency is obtained for unsteady and steady, well-resolved and under-resolved simulations.
Date Issued
2022-06-01
Date Acceptance
2021-04-14
Citation
Communications on Applied Mathematics and Computation, 2022, 4, pp.728-757
ISSN
2661-8893
Publisher
Springer
Start Page
728
End Page
757
Journal / Book Title
Communications on Applied Mathematics and Computation
Volume
4
Copyright Statement
© The Author(s) 2021. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
License URL
Sponsor
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Identifier
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000691313500001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
Grant Number
EP/R029423/1
EP/R023926/1
Subjects
Science & Technology
Physical Sciences
Mathematics, Applied
Mathematics
Adaptive time-stepping
Unsteady simulations
High order
Discontinuous Galerkin
Implicit time integration
DISCONTINUOUS GALERKIN METHOD
Publication Status
Published
Date Publish Online
2021-08-26