Removing Splitting/Modeling Error in Projection/Penalty Methods for Navier-Stokes Simulations with Continuous Data Assimilation
Year: 2024
Author: Elizabeth Hawkins, Leo G. Rebholz, Duygu Vargun
Communications in Mathematical Research , Vol. 40 (2024), Iss. 1 : pp. 1–29
Abstract
We study continuous data assimilation (CDA) applied to projection and penalty methods for the Navier-Stokes (NS) equations. Penalty and projection methods are more efficient than consistent NS discretizations, however are less accurate due to modeling error (penalty) and splitting error (projection). We show analytically and numerically that with measurement data and properly chosen parameters, CDA can effectively remove these splitting and modeling errors and provide long time optimally accurate solutions.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cmr.2023-0008
Communications in Mathematical Research , Vol. 40 (2024), Iss. 1 : pp. 1–29
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 29
Keywords: Navier-Stokes equations projection method penalty method continuous data assimilation.