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(tn+1)−ϵ(tn). The analysis and tests show that adapting ϵ(tn+1) in response to ∇·u(tn) 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.
Author Details
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