Year: 2023
Author: Kiera Kean, Xihui Xie, Shuxian Xu
International Journal of Numerical Analysis and Modeling, Vol. 20 (2023), Iss. 3 : pp. 407–436
Abstract
We develop, analyze and test adaptive penalty parameter methods. We prove unconditional stability for velocity when adapting the penalty parameter, $ϵ,$ and stability of the velocity time derivative under a condition on the change of the penalty parameter, $ϵ(t_{n+1}) − ϵ(t_n).$ The analysis and tests show that adapting $ϵ(t_{n+1})$ in response to $∇·u(t_n)$ removes the problem of picking $ϵ$ and yields good approximations for the velocity. We provide error analysis and numerical tests to support these results. We supplement the adaptive-$ϵ$ method by also adapting the time-step. The penalty parameter ϵ and time-step are adapted independently. We further compare first, second and variable order time-step algorithms. Accurate recovery of pressure remains an open problem.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ijnam2023-1017
International Journal of Numerical Analysis and Modeling, Vol. 20 (2023), Iss. 3 : pp. 407–436
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 30
Keywords: Navier-Stokes equations penalty adaptive.