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A Doubly Adaptive Penalty Method for the Navier Stokes Equations

A Doubly Adaptive Penalty Method for the Navier Stokes Equations

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

Kiera Kean

Xihui Xie

Shuxian Xu

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    https://doi.org/10.1002/num.70002 [Citations: 0]